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Journal articles on the topic 'Tuples of Operators'

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Published: 6 September 2023

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1

Wang, Wei, Yonglu Shu, and Xingzhong Wang. "S-Mixing Tuple of Operators on Banach Spaces." Journal of Function Spaces 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/9251672.

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We consider the question: what is the appropriate formulation of Godefroy-Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators,S-mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to beS-mixing. Moreover, we study some new properties ofS-mixing operators on several concrete Banach spaces.

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2

Hoffmann, Philipp H. W., and Michael Mackey. "(m, p)-isometric and (m, ∞)-isometric operator tuples on normed spaces." Asian-European Journal of Mathematics 08, no. 02 (June 2015): 1550022. http://dx.doi.org/10.1142/s1793557115500229.

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We generalize the notion of m-isometric operator tuples on Hilbert spaces in a natural way to operator tuples on normed spaces. This is done by defining a tuple analogue of (m, p)-isometric operators, so-called (m, p)-isometric operator tuples. We then extend this definition further by introducing (m, ∞)-isometric operator tuples and study properties of and relations between these objects.

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3

Ahmed, Ahmed. "Higher dimensional [m,C]-isometric commuting d-tuple of operators." Filomat 36, no. 12 (2022): 4173–84. http://dx.doi.org/10.2298/fil2212173a.

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In this paper we recover an [m,C]-isometric operators and (m,C)-isometric commuting tuples of operators on a Hilbert space studied respectively in [11] and [16], we introduce the class of [m,C]-isometries for tuple of commuting operators. This is a generalization of the class of [m,C]-isometric commuting operators on a Hilbert spaces. A commuting tuples of operators S = (S1,..., Sp) ? B(H)p is said to be [m,C]-isometric p-tuple of commuting operators if ?m (S,C):= ?m j=0 (?1)m?j (m j) (? |?|=j j!/?! CS?CS?)=0 for some positive integer m and some conjugation C. We consider a multi-variable generalization of these single variable [m,C]-isometric operators and explore some of their basic properties.

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4

Mićić, Jadranka, Zlatko Pavić, and Josip Pečarić. "Extension of Jensen's Inequality for Operators without Operator Convexity." Abstract and Applied Analysis 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/358981.

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We give an extension of Jensen's inequality for -tuples of self-adjoint operators, unital -tuples of positive linear mappings, and real-valued continuous convex functions with conditions on the operators' bounds. We also study operator quasiarithmetic means under the same conditions.

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5

Duggal, B. P. "Subspace gaps and Weyl's theorem for an elementary operator." International Journal of Mathematics and Mathematical Sciences 2005, no. 3 (2005): 465–74. http://dx.doi.org/10.1155/ijmms.2005.465.

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A range-kernal orthogonality property is established for the elementary operatorsℰ(X)=∑i=1nAiXBiandℰ*(X)=∑i=1nAi*XBi*, whereA=(A1,A2,…,An)andB=(B1,B2,…,Bn)aren-tuples of mutually commuting scalar operators (in the sense of Dunford) in the algebraB(H)of operators on a Hilbert spaceH. It is proved that the operatorℰsatisfies Weyl's theorem in the case in whichAandBaren-tuples of mutually commuting generalized scalar operators.

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6

Charlesworth, Ian, Ken Dykema, Fedor Sukochev, and Dmitriy Zanin. "Simultaneous Upper Triangular Forms for Commuting Operators in a Finite von Neumann Algebra." Canadian Journal of Mathematics 72, no. 5 (May 15, 2019): 1188–245. http://dx.doi.org/10.4153/s0008414x19000282.

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AbstractThe joint Brown measure and joint Haagerup–Schultz projections for tuples of commuting operators in a von Neumann algebra equipped with a faithful tracial state are investigated, and several natural properties are proved for these. It is shown that the support of the joint Brown measure is contained in the Taylor joint spectrum of the tuple, and also in the ostensibly smaller left Harte spectrum. A simultaneous upper triangularization result for finite commuting tuples is proved, and the joint Brown measure and joint Haagerup–Schultz projections are shown to behave well under the Arens multivariate holomorphic functional calculus of such a commuting tuple.

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7

Chō, Muneo. "Joint spectra of commuting normal operators on Banach spaces." Glasgow Mathematical Journal 30, no. 3 (September 1988): 339–45. http://dx.doi.org/10.1017/s0017089500007436.

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The joint spectrum for a commuting n-tuple in functional analysis has its origin in functional calculus which appeared in J. L. Taylor's epoch-making paper [19] in 1970. Since then, many papers have been published on commuting n-tuples of operators on Hilbert spaces (for example, [3], [4], [5], [8], [9], [10], [21], [22]).

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8

Bhatia, R., and L. Elsner. "On Joint Eigenvalues of Commuting Matrices." Canadian Mathematical Bulletin 39, no. 2 (June 1, 1996): 164–68. http://dx.doi.org/10.4153/cmb-1996-020-6.

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AbstractA spectral radius formula for commuting tuples of operators has been proved in recent years. We obtain an analog for all the joint eigenvalues of a commuting tuple of matrices. For a single matrix this reduces to an old result of Yamamoto.

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9

Works, Karen, and Elke A. Rundensteiner. "Preferential Resource Allocation in Stream Processing Systems." International Journal of Cooperative Information Systems 23, no. 04 (December 2014): 1450006. http://dx.doi.org/10.1142/s0218843014500063.

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Overloaded data stream management systems (DSMS) cannot process all tuples within their response time. For some DSMS it is crucial to allocate the precious resources to process the most significant tuples. Prior work has applied shedding and spilling to permanently drop or temporarily place to disk insignificant tuples. However neither approach considers that tuple significance can be multi-tiered nor that significance determination can be costly. These approaches consider all tuples not dropped to be equally significant. Unlike these prior works, we take a fresh stance by pulling the most significant tuples forward throughout the query pipeline. Proactive Promotion (PP), a new DSMS methodology for preferential CPU resource allocation, selectively pulls the most significant tuples ahead of less significant tuples. Our optimizer produces an optimal PP plan that minimizes the processing latency of tuples in the most significant tiers in this multi-tiered precedence scheme by strategically placing significance determination operators throughout the query pipeline at compile-time and by agilely activating them at run-time. Our results substantiate that PP lowers the latency and increases the throughput for significant results when compared to the state-of-the-art shedding and traditional DSMS approaches (between 2 and 18 fold for a rich diversity of datasets) with negligible overhead.

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10

Müller, Vladimir. "UNIVERSAL N-TUPLES OF OPERATORS." Mathematical Proceedings of the Royal Irish Academy 113A, no. 2 (2013): 143–50. http://dx.doi.org/10.1353/mpr.2013.0015.

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11

Beliakov, G., T. Calvo, and A. Pradera. "Absorbent tuples of aggregation operators." Fuzzy Sets and Systems 158, no. 15 (August 2007): 1675–91. http://dx.doi.org/10.1016/j.fss.2007.03.007.

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12

Altwaijry, Najla, Kais Feki, and Nicuşor Minculete. "A New Seminorm for d-Tuples of A-Bounded Operators and Their Applications." Mathematics 11, no. 3 (January 29, 2023): 685. http://dx.doi.org/10.3390/math11030685.

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The aim of this paper was to introduce and investigate a new seminorm of operator tuples on a complex Hilbert space H when an additional semi-inner product structure defined by a positive (semi-definite) operator A on H is considered. We prove the equality between this new seminorm and the well-known A-joint seminorm in the case of A-doubly-commuting tuples of A-hyponormal operators. This study is an extension of a well-known result in [Results Math 75, 93(2020)] and allows us to show that the following equalities rA(T)=ωA(T)=∥T∥A hold for every A-doubly-commuting d-tuple of A-hyponormal operators T=(T1,…,Td). Here, rA(T),∥T∥A, and ωA(T) denote the A-joint spectral radius, the A-joint operator seminorm, and the A-joint numerical radius of T, respectively.

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13

Yakubovich, Dmitry, and Sameer Chavan. "Spherical tuples of Hilbert space operators." Indiana University Mathematics Journal 64, no. 2 (2015): 577–612. http://dx.doi.org/10.1512/iumj.2015.64.5471.

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14

Bhattacharyya, Tirthankar. "On tuples of commuting compact operators." Publications of the Research Institute for Mathematical Sciences 32, no. 5 (1996): 785–95. http://dx.doi.org/10.2977/prims/1195162382.

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15

Soltani, R., K. Hedayatian, and B. Khani Robati. "On Supercyclicity of Tuples of Operators." Bulletin of the Malaysian Mathematical Sciences Society 38, no. 4 (December 17, 2014): 1507–16. http://dx.doi.org/10.1007/s40840-014-0083-z.

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16

Amor, Ali Ben. "An extension of Henrici theorem for the joint approximate spectrum of commuting spectral operators." Journal of the Australian Mathematical Society 75, no. 2 (October 2003): 233–46. http://dx.doi.org/10.1017/s1446788700003748.

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AbstractGiven two m-tuples of commuting spectral operators on a Hilbert space, T = (T1,…, Tm) and S = (S1,…, Sm), an extended version of Henrici perturbation theorem is obtained for the joint approximate spectrum of S under perturbation by T. We also derive an extended version of Bauer-Fike theorem for such tuples of operators. The method used involves Clifford algebra techniques introduced by McIntosh and Pryde.

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17

Rudol, K. "The spectrum of orthogonal sums of subnormal pairs." Glasgow Mathematical Journal 30, no. 1 (January 1988): 11–15. http://dx.doi.org/10.1017/s0017089500006984.

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This note provides yet another example of the difficulties that arise when one wants to extend the spectral theory of subnormal operators to subnormal tuples. Several basic properties of a subnormal operator Y remain true for tuples; e.g. the existence and uniqueness of its minimal normal extension N, the spectral inclusion σ(N)⊂ σ(Y)-proved for n-tuples in [4] and generalized to infinite tuples in [5]. However, neither the invariant subspace theorem nor the spectral mapping theorem in the “strong form” as in [3] is known so far for subnormal tuples.

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18

Müller, V., and Yu Tomilov. "Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov." Concrete Operators 7, no. 1 (August 20, 2020): 133–54. http://dx.doi.org/10.1515/conop-2020-0102.

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AbstractWe present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks. Thereafter, numerical ranges techniques will be applied to various problems of operator theory. In particular, we discuss problems concerning orbits of operators, diagonals of operators and their tuples, and pinching problems. Lastly, motivated by known results on the numerical radius of a single operator, we examine whether, given bounded linear operators T1, . . ., Tn on a Hilbert space H, there exists a unit vector x ∈ H such that |〈Tjx, x〉| is “large” for all j = 1, . . . , n.

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19

Conway, John B., and Jim Gleason. "Absolute Equivalence and Dirac Operators of Commuting Tuples of Operators." Integral Equations and Operator Theory 51, no. 1 (January 2005): 57–71. http://dx.doi.org/10.1007/s00020-003-1255-7.

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20

Hoffmann, Philipp. "On (m, p)-isometric operators and operator tuples on normed spaces." Irish Mathematical Society Bulletin 0072 (2013): 31–32. http://dx.doi.org/10.33232/bims.0072.31.32.

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21

Kerchy, Laszlo. "Quasianalytic n-tuples of Hilbert space operators." Journal of Operator Theory 81, no. 1 (December 15, 2018): 3–20. http://dx.doi.org/10.7900/jot.2017sep07.2205.

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The residual and ∗-residual parts of the unitary dilation proved to be especially useful in the study of contractions. A more direct approach to these components, originated in B. Sz.-Nagy, \textit{Acta Sci. Math. (Szeged)} \textbf{11}(1947), 152--157, leads to the concept of unitary asymptote, and opens the way for generalizations to more general settings. In this paper a systematic study of unitary asymptotes of commuting n-tuples of general Hilbert space operators is initiated. Special emphasis is put on the study of the quasianalyticity property, which constitutes homogeneous behaviour in localization, and plays a crucial role in the quest for proper hyperinvariant subspaces.

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22

Guterman, A. E., and P. M. Shteyner. "Linear Operators Preserving Majorization of Matrix Tuples." Vestnik St. Petersburg University, Mathematics 53, no. 2 (April 2020): 136–44. http://dx.doi.org/10.1134/s1063454120020077.

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23

Guterman, Alexander E., and Pavel M. Shteyner. "Linear operators preserving majorization of matrix tuples." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 7 (65), no. 2 (2020): 217–29. http://dx.doi.org/10.21638/11701/spbu01.2020.204.

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24

Fedotov, S. N. "Framed moduli spaces and tuples of operators." Journal of Mathematical Sciences 193, no. 4 (August 10, 2013): 606–21. http://dx.doi.org/10.1007/s10958-013-1488-1.

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25

Shkarin, Stanislav. "Hypercyclic tuples of operators on ℂnand ℝn." Linear and Multilinear Algebra 60, no. 8 (August 2012): 885–96. http://dx.doi.org/10.1080/03081087.2010.533174.

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26

Müller, Vladimir. "Universal N-Tuples of Operators." Mathematical Proceedings of the Royal Irish Academy 113, no. 2 (January 1, 2013): 143–50. http://dx.doi.org/10.3318/pria.2013.113.13.

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27

Bhatia, Rajendra, Ludwig Elsner, and Peter ?emrl. "Distance between commuting tuples of normal operators." Archiv der Mathematik 71, no. 3 (September 1, 1998): 229–32. http://dx.doi.org/10.1007/s000130050257.

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28

Altwaijry, Najla, Silvestru Sever Dragomir, and Kais Feki. "Inequalities and Reverse Inequalities for the Joint A-Numerical Radius of Operators." Axioms 12, no. 3 (March 22, 2023): 316. http://dx.doi.org/10.3390/axioms12030316.

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In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius for d=1. Here, A is a positive operator on H. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated.

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29

Jeon, In Ho. "On joint essential spectra of doubly commuting n-tuples of p-hyponormal operators." Glasgow Mathematical Journal 40, no. 3 (September 1998): 353–58. http://dx.doi.org/10.1017/s0017089500032705.

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AbstractLet A be an operator on a Hillbert space with polar decomposition A = |A|, let Â = |A|½U|A|½ and let Â = V|Â| be the polar decomposition of Â. Write Ã for the operatorÃ = |Â|½V|Â|½. If = (A1,…,AN) is a doubly commuting n-tuple of p-hyponormal operators on a Hillbert space with equal defect and nullity, then = (Ã1,…,Ãn) is a doubly commuting n-tuple of hyponormal operators. In this paper we show thatwhere σ* denotes σTe (Taylor essential spectrum), σTw (Taylor-Weyl spectrum) and σTb (Taylor-Browder spectrum), respectively.

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30

Hladnik, Milan. "Spectrality of elementary operators." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 49, no. 2 (October 1990): 327–46. http://dx.doi.org/10.1017/s1446788700030603.

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AbstractSpectrality and prespectrality of elementary operators , acting on the algebra B(k) of all bounded linear operators on a separable infinite-dimensional complex Hubert space K, or on von Neumann-Schatten classes in B(k), are treated. In the case when (a1, a2, …, an) and (b1, b2, …, bn) are two n—tuples of commuting normal operators on H, the complete characterization of spectrality is given.

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31

Ahmed Mahmoud, Sid Ahmed Ould, Ahmed Himadan Ahmed, and Ahmad Sarosh. "α , β -Normal Operators in Several Variables." Mathematical Problems in Engineering 2022 (June 15, 2022): 1–11. http://dx.doi.org/10.1155/2022/3020449.

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We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality, and quasi-hyponormality to joint quasi-hyponormality.

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32

Friedrich, J. "On tuples of commuting symmetric, non-selfadjoint operators." Integral Equations and Operator Theory 13, no. 4 (July 1990): 553–75. http://dx.doi.org/10.1007/bf01210401.

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33

Feldman, Nathan S. "Hypercyclic tuples of operators and somewhere dense orbits." Journal of Mathematical Analysis and Applications 346, no. 1 (October 2008): 82–98. http://dx.doi.org/10.1016/j.jmaa.2008.04.027.

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34

Nazarov, Fedor, and Vladimir Peller. "Functions of perturbed tuples of self-adjoint operators." Comptes Rendus Mathematique 350, no. 7-8 (April 2012): 349–54. http://dx.doi.org/10.1016/j.crma.2012.04.010.

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35

Xia, Daoxing. "A Commutator Formula for Subnormal Tuples of Operators." Integral Equations and Operator Theory 83, no. 3 (May 9, 2015): 381–92. http://dx.doi.org/10.1007/s00020-015-2238-1.

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36

Duggal, B. P. "On the spectrum of n-tuples of p-hyponormal operators." Glasgow Mathematical Journal 40, no. 1 (March 1998): 123–31. http://dx.doi.org/10.1017/s0017089500032419.

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Let B(H) denote the algebra of operators (i.e., bounded linear transformations) on the Hilbert space H. A ∈ B (H) is said to be p-hyponormal (0<p<l), if (AA*)γ < (A*A)p. (Of course, a l-hyponormal operator is hyponormal.) The p-hyponormal property is monotonic decreasing in p and a p-hyponormal operator is q-hyponormal operator for all 0<q <p. Let A have the polar decomposition A = U |A|, where U is a partial isometry and |A| denotes the (unique) positive square root of A*A.If A has equal defect and nullity, then the partial isometry U may be taken to be unitary. Let ℋU(p) denote the class of p -hyponormal operators for which U in A = U |A| is unitary. ℋU(l/2) operators were introduced by Xia and ℋU(p) operators for a general 0<p<1 were first considered by Aluthge (see [1,14]); ℋU(p) operators have since been considered by a number of authors (see [3, 4, 5, 9, 10] and the references cited in these papers). Generally speaking, ℋU(p) operators have spectral properties similar to those of hyponormal operators. Indeed, let A ε ℋU(p), (0<p <l/2), have the polar decomposition A = U|A|, and define the ℋW(p + 1/2) operator Â by A = |A|1/2U |A|l/2 Let Â = V |Â| Â= |Â|1/2VÂ|ÂAcirc;|1/2. Then we have the following result.

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37

Benczúr, András, and Gyula I. Szabó. "Towards a Normal Form and a Query Language for Extended Relations Defined by Regular Expressions." Journal of Database Management 27, no. 2 (April 2016): 27–48. http://dx.doi.org/10.4018/jdm.2016040102.

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This paper introduces a generalized data base concept that unites relational and semi structured data models. As an important theoretical result we could find a quadratic decision algorithm for the implication problem of functional and join dependencies defined on the united data model. As practical contribution we presented a normal form for the new data model as a tool for data base design. With our novel representations of regular expressions, a more effective searching method could be developed. XML elements are described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a semi-structured tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the non-terminal symbols. In the authors' former work (Szabó and Benczúr, 2015) they introduced the notion of the extended tuple as a sentence from a regular language generated by a grammar where the non-terminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations. The authors then introduced the dual language, which generates the tuple types allowed to occur in extended relations. They defined functional dependencies (regular FD - RFD) over extended relations. In this paper they rephrase the RFD concept by directly using regular expressions over attribute names to define extended tuples. By the help of a special vertex labeled graph associated to regular expressions the specification of substring selection for the projection operation can be defined. The normalization for regular schemas is more complex than it is in the relational model, because the schema of an extended relation can contain an infinite number of tuple types. However, the authors can define selection, projection and join operations on extended relations too, so a lossless-join decomposition can be performed. They extended their previous model to deal with XML schema indicators too, e.g., with numerical constraints. They added line and set constructors too, in order to extend their model with more general projection and selection operators. This model establishes a query language with table join functionality for collected XML element data.

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38

Xia, Daoxing. "On pure subnormal operators with finite rank self-commutators and related operator tuples." Integral Equations and Operator Theory 24, no. 1 (March 1996): 106–25. http://dx.doi.org/10.1007/bf01195487.

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39

Qiyas, Muhammad, Muhammad Naeem, Lazim Abdullah, Muhammad Riaz, and Neelam Khan. "Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator." Symmetry 15, no. 1 (January 16, 2023): 251. http://dx.doi.org/10.3390/sym15010251.

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In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

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40

Andrei, ِDiana. "Multicentric holomorphic calculus for $n-$tuples of commuting operators." Advances in Operator Theory 4, no. 2 (April 2019): 447–61. http://dx.doi.org/10.15352/aot.1804-1346.

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41

Giménez, José. "Joint spectrum of subnormal $n$-tuples of composition operators." Proceedings of the American Mathematical Society 130, no. 7 (December 27, 2001): 2015–23. http://dx.doi.org/10.1090/s0002-9939-01-06304-3.

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42

Jury, Michael T., and David W. Kribs. "Partially isometric dilations of noncommuting $N$-tuples of operators." Proceedings of the American Mathematical Society 133, no. 1 (June 23, 2004): 213–22. http://dx.doi.org/10.1090/s0002-9939-04-07547-1.

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43

Kissin, Edward. "On Clarkson-McCarthy inequalities for $n$-tuples of operators." Proceedings of the American Mathematical Society 135, no. 08 (March 14, 2007): 2483–96. http://dx.doi.org/10.1090/s0002-9939-07-08710-2.

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44

Chō, Muneo, Raúl E. Curto, and Tadasi Huruya. "n-Tuples of operators satisfying σT(AB)=σT(BA)." Linear Algebra and its Applications 341, no. 1-3 (January 2002): 291–98. http://dx.doi.org/10.1016/s0024-3795(01)00407-4.

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45

Hirzallah, Omar, and Fuad Kittaneh. "Non-commutative Clarkson Inequalities for n-Tuples of Operators." Integral Equations and Operator Theory 60, no. 3 (February 9, 2008): 369–79. http://dx.doi.org/10.1007/s00020-008-1565-x.

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46

Hoseini M., S. Nasrin, and Mezban Habibi. "On hypercyclicity \infty-tuples of commutative bounded linear operators." Pure Mathematical Sciences 3 (2014): 17–21. http://dx.doi.org/10.12988/pms.2014.359.

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47

Bagchi, Bhaskar, and Gadadhar Misra. "Homogeneous Tuples of Multiplication Operators on Twisted Bergman Spaces." Journal of Functional Analysis 136, no. 1 (February 1996): 171–213. http://dx.doi.org/10.1006/jfan.1996.0026.

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48

Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "A Functional Calculus for n-Tuples of Noncommuting Operators." Advances in Applied Clifford Algebras 19, no. 2 (March 19, 2009): 225–36. http://dx.doi.org/10.1007/s00006-009-0163-6.

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Gerhold, Malte, and Orr Moshe Shalit. "On the matrix range of random matrices." Journal of Operator Theory 85, no. 2 (March 15, 2021): 527–45. http://dx.doi.org/10.7900/jot.2019dec04.2277.

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Abstract:

This note treats a simple minded question: \textit{what does a typical random matrix range look like?} We study the relationship between various modes of convergence for tuples of operators on the one hand, and continuity of matrix ranges with respect to the Hausdorff metric on the other. In particular, we show that the matrix range of a tuple generating a continuous field of C∗-algebras is continuous in the sense that every level is continuous in the Hausdorff metric. Using this observation together with known results on strong convergence in distribution of matrix ensembles, we identify the limit matrix ranges to which the matrix ranges of independent Wigner or Haar ensembles converge.

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50

Cobos, Fernando, Luz M. Fernández-Cabrera, and Joaquim Martín. "Some reiteration results for interpolation methods defined by means of polygons." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 138, no. 6 (November 12, 2008): 1179–95. http://dx.doi.org/10.1017/s0308210507000315.

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Abstract:

We continue the research on reiteration results between interpolation methods associated to polygons and the real method. Applications are given to N-tuples of function spaces, of spaces of bounded linear operators and Banach algebras.

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