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Journal articles on the topic 'C*-algebra'

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Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

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1

Loring, Terry A. "$C^*$-Algebra relations." MATHEMATICA SCANDINAVICA 107, no. 1 (September 1, 2010): 43. http://dx.doi.org/10.7146/math.scand.a-15142.

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We investigate relations on elements in $C^{*}$-algebras, including $*$-polynomial relations, order relations and all relations that correspond to universal $C^{*}$-algebras. We call these $C^{*}$-relations and define them axiomatically. Within these are the compact $C^{*}$-relations, which are those that determine universal $C^{*}$-algebras, and we introduce the more flexible concept of a closed $C^{*}$-relation. In the case of a finite set of generators, we show that closed $C^{*}$-relations correspond to the zero-sets of elements in a free $\sigma$-$C^{*}$-algebra. This provides a solid link between two of the previous theories on relations in $C^{*}$-algebras. Applications to lifting problems are briefly considered in the last section.

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2

Murphy, Gerald J. "The C*-Algebra of a Function Algebra." Integral Equations and Operator Theory 47, no. 3 (November 1, 2003): 361–74. http://dx.doi.org/10.1007/s00020-002-1167-y.

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3

Wei, Xiaomin, Lining Jiang, and Dianlu Tian. "The Crossed Product of Finite Hopf C*-Algebra and C*-Algebra." Mathematics 9, no. 9 (May 1, 2021): 1023. http://dx.doi.org/10.3390/math9091023.

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Let H be a finite Hopf C*-algebra and A a C*-algebra of finite dimension. In this paper, we focus on the crossed product A⋊H arising from the action of H on A, which is a ∗-algebra. In terms of the faithful positive Haar measure on a finite Hopf C*-algebra, one can construct a linear functional on the ∗-algebra A⋊H, which is further a faithful positive linear functional. Here, the complete positivity of a positive linear functional plays a vital role in the argument. At last, we conclude that the crossed product A⋊H is a C*-algebra of finite dimension according to a faithful ∗- representation.

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4

Somerset, D. "The local multiplier algebra of A C=*=-algebra." Quarterly Journal of Mathematics 47, no. 185 (March 1, 1996): 123–32. http://dx.doi.org/10.1093/qjmath/47.185.123.

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5

Bice, Tristan, and Alessandro Vignati. "$C^*$-algebra distance filters." Advances in Operator Theory 3, no. 3 (April 2018): 655–81. http://dx.doi.org/10.15352/aot.1710-1241.

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6

Fattahi, Fatemeh. "Fuzzy Quasi C*-algebra." Fuzzy Information and Engineering 5, no. 3 (September 2013): 327–33. http://dx.doi.org/10.1007/s12543-013-0152-2.

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7

Arklint, Sara E. "Hereditary C∗-subalgebras of graph C∗-algebras." Journal of Operator Theory 84, no. 1 (May 15, 2020): 99–126. http://dx.doi.org/10.7900/jot.2019jan21.2230.

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We show that a C∗-algebra A which is stably isomorphic to a unital graph C∗-algebra, is isomorphic to a graph C∗-algebra if and only if it admits an approximate unit of projections. As a consequence, a hereditary C∗-subalgebra of a unital real rank zero graph C∗-algebra is isomorphic to a graph C∗-algebra. Furthermore, if a C∗-algebra A admits an approximate unit of projections, then its minimal unitization is isomorphic to a graph C∗-algebra if and only if A is stably isomorphic to a unital graph C∗-algebra.

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8

Ng, P. W. "The multiplier algebra of a nuclear quasidiagonal C*-algebra." Bulletin of the London Mathematical Society 40, no. 5 (July 18, 2008): 827–37. http://dx.doi.org/10.1112/blms/bdn062.

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9

Somerset, D. W. B. "The Local Multiplier Algebra of a C*-Algebra, II." Journal of Functional Analysis 171, no. 2 (March 2000): 308–30. http://dx.doi.org/10.1006/jfan.2000.3527.

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10

Robinson, P. L. "The Even C ∗ Clifford Algebra." Proceedings of the American Mathematical Society 118, no. 3 (July 1993): 713. http://dx.doi.org/10.2307/2160109.

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11

Uuye, Otgonbayar. "Homotopical algebra for C*-algebras." Journal of Noncommutative Geometry 7, no. 4 (2013): 981–1006. http://dx.doi.org/10.4171/jncg/141.

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12

Rao, G. C., and P. Sundarayya. "Boolean Algebra of C-Algebras." ITB Journal of Sciences 44, no. 3 (2012): 204–16. http://dx.doi.org/10.5614/itbj.sci.2012.44.3.1.

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13

Shourijeh, B. Tabatabaie. "PARTIAL INVERSE SEMIGROUP $C^*$-ALGEBRA." Taiwanese Journal of Mathematics 10, no. 6 (December 2006): 1539–48. http://dx.doi.org/10.11650/twjm/1500404573.

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14

Wei, Changguo. "Homomorphisms between C*-algebra extensions." Proceedings - Mathematical Sciences 120, no. 1 (February 2010): 97–104. http://dx.doi.org/10.1007/s12044-010-0012-5.

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15

Barnich, G., R. Fulp, T. Lada, and J. Stasheff. "Algebra structures onhom(C,L)." Communications in Algebra 28, no. 11 (January 2000): 5481–501. http://dx.doi.org/10.1080/00927870008827169.

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16

Robert, Leonel, and Aaron Tikuisis. "Hilbert C*-modules over a commutative C*-algebra." Proceedings of the London Mathematical Society 102, no. 2 (July 23, 2010): 229–56. http://dx.doi.org/10.1112/plms/pdq017.

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17

Brownlee, Erin, and Benton L. Duncan. "A $$C^*$$C∗-Algebra Construction for Undirected Graphs." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 2 (January 17, 2019): 1095–110. http://dx.doi.org/10.1007/s40840-019-00726-8.

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18

Ara, Pere. "On the symmetric algebra of quotients of a C*-algebra." Glasgow Mathematical Journal 32, no. 3 (September 1990): 377–79. http://dx.doi.org/10.1017/s0017089500009460.

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Let R be a semiprime ring (possibly without 1). The symmetric ring of quotients of R is defined as the set of equivalence classes of essentially defined double centralizers (ƒ, g) on R; see [1], [8]. So, by definition, ƒ is a left R-module homomorphism from an essential ideal I of R into R, g is a right R-module homomorphism from an essential ideal J of R into R, and they satisfy the balanced condition ƒ(x)y = xg(y) for x ∈ Iand y ∈ J. This ring was used by Kharchenko in his investigations on the Galois theory of semiprime rings [4] and it is also a useful tool for the study of crossed products of prime rings [7]. We denote the symmetric ring of quotients of a semiprime ring R by Q(R).

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19

Juschenko, Kate. "Ideals of a C *-algebra generated by an operator algebra." Mathematische Zeitschrift 266, no. 3 (August 18, 2009): 693–705. http://dx.doi.org/10.1007/s00209-009-0594-8.

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20

Lin, Huaxin. "Homomorphisms From C(X) Into C*-Algebras." Canadian Journal of Mathematics 49, no. 5 (October 1, 1997): 963–1009. http://dx.doi.org/10.4153/cjm-1997-050-9.

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AbstractLet A be a simple C*-algebra with real rank zero, stable rank one and weakly unperforated K0(A) of countable rank. We show that a monomorphism Φ: C(S2) → A can be approximated pointwise by homomorphisms from C(S2) into A with finite dimensional range if and only if certain index vanishes. In particular,we show that every homomorphism ϕ from C(S2) into a UHF-algebra can be approximated pointwise by homomorphisms from C(S2) into the UHF-algebra with finite dimensional range.As an application, we show that if A is a simple C*-algebra of real rank zero and is an inductive limit of matrices over C(S2) then A is an AF-algebra. Similar results for tori are also obtained. Classification of Hom (C(X), A) for lower dimensional spaces is also studied.

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21

Kirchberg, Eberhard, and Mikael Rørdam. "When central sequence C*-algebras have characters." International Journal of Mathematics 26, no. 07 (June 2015): 1550049. http://dx.doi.org/10.1142/s0129167x15500494.

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We investigate C*-algebras whose central sequence algebra has no characters, and we raise the question if such C*-algebras necessarily must absorb the Jiang–Su algebra (provided that they also are separable). We relate this question to a question of Dadarlat and Toms if the Jiang–Su algebra always embeds into the infinite tensor power of any unital C*-algebra without characters. We show that absence of characters of the central sequence algebra implies that the C*-algebra has the so-called strong Corona Factorization Property, and we use this result to exhibit simple nuclear separable unital C*-algebras whose central sequence algebra does admit a character. We show how stronger divisibility properties on the central sequence algebra imply stronger regularity properties of the underlying C*-algebra.

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22

张, 志龙. "The Derivation Algebra of Lie Algebra Der(C_q)∝C_q." Pure Mathematics 05, no. 01 (2015): 1–7. http://dx.doi.org/10.12677/pm.2015.51001.

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23

AMINI, MASSOUD, MOHAMMAD B. ASADI, GEORGE A. ELLIOTT, and FATEMEH KHOSRAVI. "FRAMES IN HILBERT C*-MODULES AND MORITA EQUIVALENT C*-ALGEBRAS." Glasgow Mathematical Journal 59, no. 1 (August 3, 2016): 1–10. http://dx.doi.org/10.1017/s0017089516000355.

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AbstractWe show that the property of a C*-algebra that all its Hilbert modules have a frame, in the case of σ-unital C*-algebras, is preserved under Rieffel–Morita equivalence. In particular, we show that a σ-unital continuous-trace C*-algebra with trivial Dixmier–Douady class, all of whose Hilbert modules admit a frame, has discrete spectrum. We also show this for the tensor product of any commutative C*-algebra with the C*-algebra of compact operators on any Hilbert space.

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24

FUJINO, MASARU. "C*-algebras arising from substitutions." Ergodic Theory and Dynamical Systems 30, no. 6 (November 24, 2009): 1685–702. http://dx.doi.org/10.1017/s0143385709000790.

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AbstractIn this paper, we introduce a C*-algebra associated with a primitive substitution. We show that when σ is proper, the C*-algebra is simple and purely infinite and contains the associated Cuntz–Krieger algebra and the crossed product C*-algebra of the corresponding Cantor minimal system. We calculate the K-groups.

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25

PHILLIPS, N. CHRISTOPHER. "CONTINUOUS–TRACE C*-ALGEBRAS NOT ISOMORPHIC TO THEIR OPPOSITE ALGEBRAS." International Journal of Mathematics 12, no. 03 (May 2001): 263–75. http://dx.doi.org/10.1142/s0129167x01000642.

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We give examples of locally trivial continuous-trace C *-algebra not isomorphic to their opposite algebras. Our examples include a unital C *-algebra which is both stably isomorphic to and homotopy equivalent to its opposite algebra, a unital C *-algebra which is homotopy equivalent to but not stably isomorphic to its opposite algebra, and a unital C *-algebra which is not even stably homotopy equivalent to its opposite algebra.

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26

Amini, Massoud. "Locally Compact Pro-C*-Algebras." Canadian Journal of Mathematics 56, no. 1 (February 1, 2004): 3–22. http://dx.doi.org/10.4153/cjm-2004-001-6.

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AbstractLet X be a locally compact non-compact Hausdorff topological space. Consider the algebras C(X), Cb(X), C0(X), and C00(X) of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions on X. Of these, the second and third are C*-algebras, the fourth is a normed algebra, whereas the first is only a topological algebra (it is indeed a pro-C*- algebra). The interesting fact about these algebras is that if one of them is given, the others can be obtained using functional analysis tools. For instance, given the C*-algebra C0(X), one can get the other three algebras by C00(X) = K(C0(X)), Cb(X) = M(C0(X)), C(X) = Γ(K(C0(X))), where the right hand sides are the Pedersen ideal, the multiplier algebra, and the unbounded multiplier algebra of the Pedersen ideal of C0(X), respectively. In this article we consider the possibility of these transitions for general C*-algebras. The difficult part is to start with a pro-C*-algebra A and to construct a C*-algebra A0 such that A = Γ(K(A0)). The pro-C*-algebras for which this is possible are called locally compact and we have characterized them using a concept similar to that of an approximate identity.

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27

Phillips, N. Christopher. "A simple separable C*-algebra not isomorphic to its opposite algebra." Proceedings of the American Mathematical Society 132, no. 10 (June 2, 2004): 2997–3005. http://dx.doi.org/10.1090/s0002-9939-04-07330-7.

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28

Tang, Xiaomin, and Yang Zhang. "Post-Lie algebra structures on solvable Lie algebra t(2,C)." Linear Algebra and its Applications 462 (December 2014): 59–87. http://dx.doi.org/10.1016/j.laa.2014.08.019.

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29

Hu, Jun. "BMW algebra, quantized coordinate algebra and type $C$ Schur–Weyl duality." Representation Theory of the American Mathematical Society 15, no. 01 (January 10, 2011): 1. http://dx.doi.org/10.1090/s1088-4165-2011-00369-1.

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30

Exel, Ruy, Daniel Gonçalves, and Charles Starling. "The tiling C*-algebra viewed as a tight inverse semigroup algebra." Semigroup Forum 84, no. 2 (November 29, 2011): 229–40. http://dx.doi.org/10.1007/s00233-011-9359-x.

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31

Lin, Huaxin. "Skeleton C*-Subalgebras." Canadian Journal of Mathematics 44, no. 2 (April 1, 1992): 324–41. http://dx.doi.org/10.4153/cjm-1992-022-7.

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AbstractWe study skeleton C*-subalgebras of a given C*-algebra. We show that if A is a unital (non-unital but σ-unital) simple C*-algebra, ℳ is any unital (nonunital) matroid C* -algebra, then A contains a skeleton C*-subalgebra B with a quotient which is isomorphic to ℳ. Other results for skeleton C*-subalgebras are also obtained. Applications of these results to the structure of quasi-multipliers and perturbations of C*-algebras are given.

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32

Somerset, D. W. B. "Discontinuous homomorphisms from C*-algebras." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 1 (July 1991): 147–50. http://dx.doi.org/10.1017/s0305004100070195.

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AbstractA necessary and sufficient condition is given for a unital C*-algebra A to admit a discontinuous homomorphism into a Banach algebra which is continuous on its centre. The condition is that A must have a Glimm ideal G such that the C*-algebra A/G admits a discontinuous homomorphism into a Banach algebra.

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33

Kalyani, P. "G- Frame Operator in C* Algebra." IOSR Journal of Mathematics 12, no. 04 (April 2016): 01–04. http://dx.doi.org/10.9790/5728-1204040104.

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34

Norahun, Wondwosen Zemene, Teferi Getachew Alemayehu, and Gezahagne Mulat Addis. "Fuzzy Annihilator Ideals of C -Algebra." Advances in Fuzzy Systems 2021 (September 9, 2021): 1–10. http://dx.doi.org/10.1155/2021/7481960.

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In this paper, we introduce the concept of relative fuzzy annihilator ideals in C-algebras and investigate some its properties. We characterize relative fuzzy annihilators in terms of fuzzy points. It is proved that the class of fuzzy ideals of C-algebras forms Heything algebra. We observe that the class of all fuzzy annihilator ideals can be made as a complete Boolean algebra. Moreover, we study the concept of fuzzy annihilator preserving homomorphism. We provide a sufficient condition for a homomorphism to be a fuzzy annihilator preserving.

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35

Robinson, P. L. "The even $C\sp *$ Clifford algebra." Proceedings of the American Mathematical Society 118, no. 3 (March 1, 1993): 713. http://dx.doi.org/10.1090/s0002-9939-1993-1131039-5.

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36

Forger, Michael, and Daniel V. Paulino. "C∗-completions and the DFR-algebra." Journal of Mathematical Physics 57, no. 2 (February 2016): 023517. http://dx.doi.org/10.1063/1.4940718.

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37

Khoshkam, M., and J. Tavakoli. "Categorical constructions in C*-algebra theory." Journal of the Australian Mathematical Society 73, no. 1 (August 2002): 97–114. http://dx.doi.org/10.1017/s1446788700008491.

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AbstractThe notions of limits and colimits are studied in the category of C*-algebras. It is shown that limits and colimits of diagrams of C*-algebras are stable under tensor product by a fixed C*-algebra, and crossed product by a locally compact group.

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38

P, KALYANI. "G- Frame Operator in C* Algebra." International Journal of Mathematics Trends and Technology 66, no. 4 (April 25, 2020): 1–9. http://dx.doi.org/10.14445/22315373/ijmtt-v66i4p501.

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39

Meltem Erden; ALACA, EGE. "C*-algebra-valued s-metric spaces." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 67, no. 2 (2018): 165–77. http://dx.doi.org/10.1501/commua1_0000000871.

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40

Li, Liangqing. "C*-Algebra Homomorphisms and kk-Theory." K-Theory 18, no. 2 (October 1999): 161–72. http://dx.doi.org/10.1023/a:1007743325440.

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41

Arveson, W. "C*-Algebras and Numerical Linear Algebra." Journal of Functional Analysis 122, no. 2 (June 1994): 333–60. http://dx.doi.org/10.1006/jfan.1994.1072.

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42

Higson, N. "C*-Algebra Extension Theory and Duality." Journal of Functional Analysis 129, no. 2 (May 1995): 349–63. http://dx.doi.org/10.1006/jfan.1995.1054.

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43

Hines, Taylor, and Erik Walsberg. "Nontrivially Noetherian $C^*$-algebras." MATHEMATICA SCANDINAVICA 111, no. 1 (September 1, 2012): 135. http://dx.doi.org/10.7146/math.scand.a-15219.

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We say that a $C^*$-algebra is Noetherian if it satisfies the ascending chain condition for two-sided closed ideals. A nontrivially Noetherian $C^*$-algebra is one with infinitely many ideals. Here, we show that nontrivially Noetherian $C^*$-algebras exist, and that a separable $C^*$-algebra is Noetherian if and only if it contains countably many ideals and has no infinite strictly ascending chain of primitive ideals. Furthermore, we prove that every Noetherian $C^*$-algebra has a finite-dimensional center. Where possible, we extend results about the ideal structure of $C^*$-algebras to Artinian $C^*$-algebras (those satisfying the descending chain condition for closed ideals).

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44

ASADI, M. B., M. FRANK, and Z. HASSANPOUR-YAKHDANI. "FRAME-LESS HILBERT C*-MODULES." Glasgow Mathematical Journal 61, no. 1 (February 7, 2018): 25–31. http://dx.doi.org/10.1017/s0017089518000010.

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AbstractWe show that if A is a compact C*-algebra without identity that has a faithful *-representation in the C*-algebra of all compact operators on a separable Hilbert space and its multiplier algebra admits a minimal central projection p such that pA is infinite-dimensional, then there exists a Hilbert A1-module admitting no frames, where A1 is the unitization of A. In particular, there exists a frame-less Hilbert C*-module over the C*-algebra $K(\ell^2) \dotplus \mathbb{C}I_{\ell^2}$.

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45

LYKOVA, ZINAIDA A. "Relations between the homologies of C*-algebras and their commutative C*-subalgebras." Mathematical Proceedings of the Cambridge Philosophical Society 132, no. 1 (January 2002): 155–68. http://dx.doi.org/10.1017/s0305004101005497.

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The paper concerns the identification of projective closed ideals of C*-algebras. We prove that, if a C*-algebra has the property that every closed left ideal is projective, then the same is true for all its commutative C*-subalgebras. Further, we say a Banach algebra A is hereditarily projective if every closed left ideal of A is projective. As a corollary of the stated result we show that no infinite-dimensional AW*-algebra is hereditarily projective. We also prove that, for a commutative C*-algebra A contained in [Bscr ](H), where H is a separable Hilbert space, the following conditions are equivalent: (i) A is separable; and (ii) the C*-tensor product A [otimes ]minA is hereditarily projective. Howerever, there is a non-separable, hereditarily projective, commutative C*-algebra A contained in [Bscr ](H), where H is a separable Hilbert space.

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46

Jamjoom, Fatmah B. "The connection between the universal enveloping C*-algebra and the universal enveloping von Neumann algebra of a JW-algebra." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 3 (November 1992): 575–79. http://dx.doi.org/10.1017/s0305004100071255.

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AbstractThis article aims to study the relationship between the universal enveloping C*-algebra C*(M) and the universal enveloping von Neumann algebra W*(M), when M is a JW-algebra. In our main result (Theorem 2·7) we show that C*(M) can be realized as the C*-subalgebra of W*(M) generated by M.

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47

BOKUT, L. A., YUQUN CHEN, and JIAPENG HUANG. "GRÖBNER–SHIRSHOV BASES FOR L-ALGEBRAS." International Journal of Algebra and Computation 23, no. 03 (April 16, 2013): 547–71. http://dx.doi.org/10.1142/s0218196713500094.

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In this paper, we first establish Composition-Diamond lemma for Ω-algebras. We give a Gröbner–Shirshov basis of the free L-algebra as a quotient algebra of a free Ω-algebra, and then the normal form of the free L-algebra is obtained. Second we establish Composition-Diamond lemma for L-algebras. As applications, we give Gröbner–Shirshov bases of the free dialgebra and the free product of two L-algebras, and then we show four embedding theorems of L-algebras: (1) Every countably generated L-algebra can be embedded into a two-generated L-algebra. (2) Every L-algebra can be embedded into a simple L-algebra. (3) Every countably generated L-algebra over a countable field can be embedded into a simple two-generated L-algebra. (4) Three arbitrary L-algebras A, B, C over a field k can be embedded into a simple L-algebra generated by B and C if |k| ≤ dim (B * C) and |A| ≤ |B * C|, where B * C is the free product of B and C.

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48

Li, Hui, and Dilian Yang. "Boundary Quotient -algebras of Products of Odometers." Canadian Journal of Mathematics 71, no. 1 (January 7, 2019): 183–212. http://dx.doi.org/10.4153/cjm-2017-034-5.

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AbstractIn this paper, we study the boundary quotient $\text{C}^{\ast }$-algebras associated with products of odometers. One of our main results shows that the boundary quotient $\text{C}^{\ast }$-algebra of the standard product of $k$ odometers over $n_{i}$-letter alphabets $(1\leqslant i\leqslant k)$ is always nuclear, and that it is a UCT Kirchberg algebra if and only if $\{\ln n_{i}:1\leqslant i\leqslant k\}$ is rationally independent, if and only if the associated single-vertex $k$-graph $\text{C}^{\ast }$-algebra is simple. To achieve this, one of our main steps is to construct a topological $k$-graph such that its associated Cuntz–Pimsner $\text{C}^{\ast }$-algebra is isomorphic to the boundary quotient $\text{C}^{\ast }$-algebra. Some relations between the boundary quotient $\text{C}^{\ast }$-algebra and the $\text{C}^{\ast }$-algebra $\text{Q}_{\mathbb{N}}$ introduced by Cuntz are also investigated.

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49

JORGENSEN, PALLE E. T., and XIU-CHI QUAN. "COVARIANCE GROUP C*-ALGEBRAS AND GALOIS CORRESPONDENCE." International Journal of Mathematics 02, no. 06 (December 1991): 673–99. http://dx.doi.org/10.1142/s0129167x91000375.

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The main purpose of this paper is to establish a Galois correspondence for a given covariant group system, its associated C*-algebra and Hopf C*-algebra. On the way to this, we first study covariance group C*-algebras and their representations, and prove a result which is simpler but yet very similar to the C*-algebra case in the main body of the paper. We then show that there is a Galois correspondence between the lattice of normal subgroups of the given covariant group system and a corresponding lattice of certain invariant *-subalgebras of the covariant group C*-algebra; in particular, there is a natural Galois correspondence for the group C*-algebra. We further study this Galois correspondence for the Hopf C*-algebras associated with covariant group systems.

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50

Kusuda, Masaharu. "Three-space problems in discrete spectra of C*-algebras and dual C*-algebras." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 3 (June 2001): 701–7. http://dx.doi.org/10.1017/s0308210500001050.

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We discuss the three-space problem on discreteness for the Jacobson topology on the spectrum of a C*-algebra in detail. As an application, it is shown that a C*-algebra A is a dual C*-algebra if and only if a closed ideal I of A and the quotient A/I are dual C*-algebras and the open central projection, in the second dual of A, corresponding to I is a multiplier for A.

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