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Journal articles on the topic 'Spectral spaces'

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Published: 6 September 2023

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1

Ramanath, Rajeev, Rolf G. Kuehni, Wesley E. Snyder, and David Hinks. "Spectral spaces and color spaces." Color Research & Application 29, no. 1 (2003): 29–37. http://dx.doi.org/10.1002/col.10211.

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2

Echi, Othman, and Tarek Turki. "Spectral primal spaces." Journal of Algebra and Its Applications 18, no. 02 (February 2019): 1950030. http://dx.doi.org/10.1142/s0219498819500300.

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Let [Formula: see text] be a mapping. Consider [Formula: see text] Then, according to Echi, [Formula: see text] is an Alexandroff topology. A topological space [Formula: see text] is called a primal space if its topology coincides with an [Formula: see text] for some mapping [Formula: see text]. We denote by [Formula: see text] the set of all fixed points of [Formula: see text], and [Formula: see text] the set of all periodic points of [Formula: see text]. The topology [Formula: see text] induces a preorder [Formula: see text] defined on [Formula: see text] by: [Formula: see text] if and only if [Formula: see text], for some integer [Formula: see text]. The main purpose of this paper is to provide necessary and sufficient algebraic conditions on the function [Formula: see text] in order to get [Formula: see text] (respectively, the one-point compactification of [Formula: see text]) a spectral topology. More precisely, we show the following results. (1) [Formula: see text] is spectral if and only if [Formula: see text] is a finite set and every chain in the ordered set [Formula: see text] is finite. (2) The one-point(Alexandroff) compactification of [Formula: see text] is a spectral topology if and only if [Formula: see text] and every nonempty chain of [Formula: see text] has a least element. (3) The poset [Formula: see text] is spectral if and only if every chain is finite. As an application the main theorem [12, Theorem 3. 5] of Echi–Naimi may be derived immediately from the general setting of the above results.
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3

Belaid, Karim, Othman Echi, and Riyadh Gargouri. "A-spectral spaces." Topology and its Applications 138, no. 1-3 (March 2004): 315–22. http://dx.doi.org/10.1016/j.topol.2003.08.009.

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4

Belaid, Karim. "H-spectral spaces." Topology and its Applications 153, no. 15 (September 2006): 3019–23. http://dx.doi.org/10.1016/j.topol.2006.01.009.

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5

Acosta, Lorenzo, and Ibeth Marcela Rubio Perilla. "Nearly spectral spaces." Boletín de la Sociedad Matemática Mexicana 25, no. 3 (May 31, 2018): 687–700. http://dx.doi.org/10.1007/s40590-018-0206-x.

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6

Echi, Othman, and Sami Lazaar. "UNIVERSAL SPACES, TYCHONOFF AND SPECTRAL SPACES." Mathematical Proceedings of the Royal Irish Academy 109A, no. 1 (2009): 35–48. http://dx.doi.org/10.1353/mpr.2009.0014.

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7

Fontana, Marco, and Francesco Pappalardi. "The prime spaces as spectral spaces." Annali di Matematica Pura ed Applicata 160, no. 1 (December 1991): 331–45. http://dx.doi.org/10.1007/bf01764133.

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8

Echi, Othman, and Sami Lazaar. "UNIVERSAL SPACES, TYCHONOFF AND SPECTRAL SPACES." Mathematical Proceedings of the Royal Irish Academy 109, no. 1 (January 1, 2009): 35–48. http://dx.doi.org/10.3318/pria.2008.109.1.35.

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9

Peterson, Eric. "Coalgebraic formal curve spectra and spectral jet spaces." Geometry & Topology 24, no. 1 (March 25, 2020): 1–47. http://dx.doi.org/10.2140/gt.2020.24.1.

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10

Adams, M. E., Karim Belaid, Lobna Dridi, and Othman Echi. "SUBMAXIMAL AND SPECTRAL SPACES." Mathematical Proceedings of the Royal Irish Academy 108A, no. 2 (2008): 137–47. http://dx.doi.org/10.1353/mpr.2008.0008.

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11

Adams, M. E., Karim Belaid, Lobna Dridi, and Othman Echi. "SUBMAXIMAL AND SPECTRAL SPACES." Mathematical Proceedings of the Royal Irish Academy 108A, no. 1 (2008): 137–47. http://dx.doi.org/10.1353/mpr.2008.0016.

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12

Abbasi, A., and D. Hassanzadeh-Lelekaami. "Modules and Spectral Spaces." Communications in Algebra 40, no. 11 (November 2012): 4111–29. http://dx.doi.org/10.1080/00927872.2011.602273.

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13

Finocchiaro, Carmelo Antonio. "Spectral Spaces and Ultrafilters." Communications in Algebra 42, no. 4 (December 7, 2013): 1496–508. http://dx.doi.org/10.1080/00927872.2012.741875.

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14

Adams, M. E., Karim Belaid, Lobna Dridi, and Othman Echi. "SUBMAXIMAL AND SPECTRAL SPACES." Mathematical Proceedings of the Royal Irish Academy 108, no. 2 (January 1, 2008): 137–47. http://dx.doi.org/10.3318/pria.2008.108.2.137.

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15

Schwartz, Niels. "Locales as spectral spaces." Algebra universalis 70, no. 1 (June 15, 2013): 1–42. http://dx.doi.org/10.1007/s00012-013-0241-4.

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16

Goswami, Amartya. "Proper spaces are spectral." Applied General Topology 24, no. 1 (April 5, 2023): 95–99. http://dx.doi.org/10.4995/agt.2023.17800.

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Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we give a new self-contained and constructible topology-independent proof of the fact that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.
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17

Belaid, Karim, Othman Echi, and Riyadh Gargouri. "Two classes of locally compact sober spaces." International Journal of Mathematics and Mathematical Sciences 2005, no. 15 (2005): 2421–27. http://dx.doi.org/10.1155/ijmms.2005.2421.

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We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN-spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN-spaces are exactly the locally spectral coherent spaces in which every compact open set has a compact closure.
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18

Laursen, K. B., and M. M. Neumann. "Asymptotic intertwining and spectral inclusions on Banach spaces." Czechoslovak Mathematical Journal 43, no. 3 (1993): 483–97. http://dx.doi.org/10.21136/cmj.1993.128413.

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19

Finocchiaro, Carmelo A., Marco Fontana, and Dario Spirito. "Spectral spaces of semistar operations." Journal of Pure and Applied Algebra 220, no. 8 (August 2016): 2897–913. http://dx.doi.org/10.1016/j.jpaa.2016.01.008.

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20

Dobbs, David E., Richard Fedder, and Marco Fontana. "G-domains and spectral spaces." Journal of Pure and Applied Algebra 51, no. 1-2 (March 1988): 89–110. http://dx.doi.org/10.1016/0022-4049(88)90080-1.

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21

Schwartz, Niels. "Spectral Reflections of Topological Spaces." Applied Categorical Structures 25, no. 6 (April 26, 2017): 1159–85. http://dx.doi.org/10.1007/s10485-017-9488-9.

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22

Donnelly, Harold, and Frederico Xavier. "Spectral stability of symmetric spaces." Mathematische Zeitschrift 253, no. 4 (February 1, 2006): 655–58. http://dx.doi.org/10.1007/s00209-005-0902-x.

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23

Ricker, W. "Spectral operators and weakly compact homomorphisms in a class of Banach Spaces." Glasgow Mathematical Journal 28, no. 2 (July 1986): 215–22. http://dx.doi.org/10.1017/s0017089500006534.

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The purpose of this note is to present certain aspects of the theory of spectral operators in Grothendieck spaces with the Dunford-Pettis property, briefly, GDP-spaces, thereby elaborating on the recent note [10].For example, the sum and product of commuting spectral operators in such spaces are again spectral operators (cf. Proposition 2.1) and a continuous linear operator is spectral if and only if it has finite spectrum (cf. Proposition 2.2). Accordingly, if a spectral operator is of finite type, then its spectrum consists entirely of eigenvalues. Furthermore, it turns out that there are no unbounded spectral operators in such spaces (cf. Proposition 2.4). As a simple application of these results we are able to determine which multiplication operators in certain function spaces are spectral operators.
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24

Führ, Hartmut, and Azita Mayeli. "Homogeneous Besov Spaces on Stratified Lie Groups and Their Wavelet Characterization." Journal of Function Spaces and Applications 2012 (2012): 1–41. http://dx.doi.org/10.1155/2012/523586.

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We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov spaceB˙p,qsin terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield the same Besov spaces. We then turn to wavelet characterizations, first via continuous wavelet transforms (which can be viewed as continuous-scale Littlewood-Paley decompositions), then via discretely indexed systems. We prove the existence of wavelet frames and associated atomic decomposition formulas for all homogeneous Besov spacesB˙p,qswith1≤p,q<∞ands∈ℝ.
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25

Langer, Heinz, Branko Najman, and Christiane Tretter. "Spectral Theory of the Klein–Gordon Equation in Krein Spaces." Proceedings of the Edinburgh Mathematical Society 51, no. 3 (October 2008): 711–50. http://dx.doi.org/10.1017/s0013091506000150.

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AbstractIn this paper the spectral properties of the abstract Klein–Gordon equation are studied. The main tool is an indefinite inner product known as the charge inner product. Under certain assumptions on the potential V, two operators are associated with the Klein–Gordon equation and studied in Krein spaces generated by the charge inner product. It is shown that the operators are self-adjoint and definitizable in these Krein spaces. As a consequence, they possess spectral functions with singularities, their essential spectra are real with a gap around 0 and their non-real spectra consist of finitely many eigenvalues of finite algebraic multiplicity which are symmetric to the real axis. One of these operators generates a strongly continuous group of unitary operators in the Krein space; the other one gives rise to two bounded semi-groups. Finally, the results are applied to the Klein–Gordon equation in ℝn.
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26

Ricker, Werner. "Spectral representation of local semigroups in locally convex spaces." Czechoslovak Mathematical Journal 35, no. 2 (1985): 248–59. http://dx.doi.org/10.21136/cmj.1985.102013.

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27

Müller, Vladimír. "Local spectral radius formula for operators in Banach spaces." Czechoslovak Mathematical Journal 38, no. 4 (1988): 726–29. http://dx.doi.org/10.21136/cmj.1988.102268.

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28

SCHWEDE, STEFAN. "Stable homotopical algebra and Γ-spaces." Mathematical Proceedings of the Cambridge Philosophical Society 126, no. 2 (March 1999): 329–56. http://dx.doi.org/10.1017/s0305004198003272.

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In this paper we advertise the category of Γ-spaces as a convenient framework for doing ‘algebra’ over ‘rings’ in stable homotopy theory. Γ-spaces were introduced by Segal [Se] who showed that they give rise to a homotopy category equivalent to the usual homotopy category of connective (i.e. (−1)-connected) spectra. Bousfield and Friedlander [BF] later provided model category structures for Γ-spaces. The study of ‘rings, modules and algebras’ based on Γ-spaces became possible when Lydakis [Ly] introduced a symmetric monoidal smash product with good homotopical properties. Here we develop model category structures for modules and algebras, set up (derived) smash products and associated spectral sequences and compare simplicial modules and algebras to their Eilenberg–MacLane spectra counterparts.
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29

Nakagami, Yoshiomi. "Spectral analysis in Kreĭ n spaces." Publications of the Research Institute for Mathematical Sciences 24, no. 3 (1988): 361–78. http://dx.doi.org/10.2977/prims/1195175032.

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30

Nakagami, Yoshiomi. "Tomita's spectral analysis in Krein spaces." Publications of the Research Institute for Mathematical Sciences 22, no. 4 (1986): 637–58. http://dx.doi.org/10.2977/prims/1195177625.

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31

Klyaeva, I. A. "Spectral Sequences of Fibre Tolerance Spaces." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 8, no. 4 (2008): 13–18. http://dx.doi.org/10.18500/1816-9791-2008-8-4-13-18.

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32

Döring, Andreas. "Spectral presheaves as quantum state spaces." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2047 (August 6, 2015): 20140247. http://dx.doi.org/10.1098/rsta.2014.0247.

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For each quantum system described by an operator algebra of physical quantities, we provide a (generalized) state space, notwithstanding the Kochen–Specker theorem. This quantum state space is the spectral presheaf . We formulate the time evolution of quantum systems in terms of Hamiltonian flows on this generalized space and explain how the structure of the spectral presheaf geometrically mirrors the double role played by self-adjoint operators in quantum theory, as quantum random variables and as generators of time evolution.
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33

Eberle, Andreas. "Spectral Gaps on Discretized Loop Spaces." Infinite Dimensional Analysis, Quantum Probability and Related Topics 06, no. 02 (June 2003): 265–300. http://dx.doi.org/10.1142/s021902570300116x.

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We study spectral gaps w.r.t. marginals of pinned Wiener measures on spaces of discrete loops (or, more generally, pinned paths) on a compact Riemannian manifold M. The asymptotic behaviour of the spectral gap as the time parameter T of the underlying Brownian bridge goes to 0 is investigated. It turns out that depending on the choice of a Riemannian metric on the base manifold, very different asymptotic behaviours can occur. For example, on discrete loop spaces over sufficiently round ellipsoids the gap grows of order α/T as T ↓ 0. The strictly positive rate α stabilizes as the discretization approaches the continuum limit. On the other extreme, if there exists a closed geodesic γ : S1 → M such that the sectional curvature on γ(S1) is strictly negative, and the loop is pinned close to γ(S1), then the gap decays of order exp (-β/T), and the decay rate β approaches +∞ as the discretization approaches the continuum limit.
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34

Eberle, Andreas. "Local spectral gaps on loop spaces." Journal de Mathématiques Pures et Appliquées 82, no. 3 (March 2003): 313–65. http://dx.doi.org/10.1016/s0021-7824(03)00003-5.

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35

Kesseböhmer, M., and T. Samuel. "Spectral metric spaces for Gibbs measures." Journal of Functional Analysis 265, no. 9 (November 2013): 1801–28. http://dx.doi.org/10.1016/j.jfa.2013.07.012.

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36

Lapid, Erez, and Stephen Rallis. "A spectral identity between symmetric spaces." Israel Journal of Mathematics 140, no. 1 (December 2004): 221–44. http://dx.doi.org/10.1007/bf02786633.

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37

Baranov, Anton, Yurii Belov, and Alexander Borichev. "Spectral synthesis in de Branges spaces." Geometric and Functional Analysis 25, no. 2 (March 13, 2015): 417–52. http://dx.doi.org/10.1007/s00039-015-0322-y.

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38

Belova, N. O. "Spectral synthesis in Sobolev weighted spaces." Mathematical Notes 56, no. 2 (August 1994): 856–58. http://dx.doi.org/10.1007/bf02110746.

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39

Lenz, Reiner, Thanh Hai Bui, and Javier Hernández-Andrés. "Group Theoretical Structure of Spectral Spaces." Journal of Mathematical Imaging and Vision 23, no. 3 (November 2005): 297–313. http://dx.doi.org/10.1007/s10851-005-0485-5.

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40

A., Abdul-Samee, Ahlam Jameel K., and Faria Ali C. "Spectral Theory in Fuzzy Normed Spaces." Journal of Al-Nahrain University Science 14, no. 2 (June 1, 2011): 178–85. http://dx.doi.org/10.22401/jnus.14.2.23.

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41

Lange, Ridgley, and Shengwang Wang. "Strongly analytic spaces in spectral decomposition." Glasgow Mathematical Journal 30, no. 3 (September 1988): 249–57. http://dx.doi.org/10.1017/s0017089500007321.

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It is now well-known that decomposable operators have a rich structure theory; in particular, an operator is decomposable iff its adjoint is [3]. There are many other criteria for decomposability [8], [9]. In Theorem 2.2 of this paper (see below) we give several new ones. Some of these (e.g. (ii), (iii)) are “relaxations” of conditions given in [7] and [8]. Assertion (vi) is a version of a result in [10]. Characterizations (iv)and (v) are novel in two respects. For instance, (v) states that an operator Tcan be “patched” together into a decomposable operator if it has an invariant subspace Y such that T | Y and the coinduced operator T | Y are both decomposable. Secondly, in this way the strongly analytic subspace appears in the theory of spectral decomposition.
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42

ZENG, QINGPING. "Five short lemmas in Banach spaces." Carpathian Journal of Mathematics 32, no. 1 (2016): 131–40. http://dx.doi.org/10.37193/cjm.2016.01.14.

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Consider a commutative diagram of bounded linear operators between Banach spaces...with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory.
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43

Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.
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44

Petersen, Dan. "A spectral sequence for stratified spaces and configuration spaces of points." Geometry & Topology 21, no. 4 (May 19, 2017): 2527–55. http://dx.doi.org/10.2140/gt.2017.21.2527.

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45

Kozlov, K. L. "Spectral decompositions of spaces induced by spectral decompositions of acting groups." Topology and its Applications 160, no. 11 (July 2013): 1188–205. http://dx.doi.org/10.1016/j.topol.2013.04.011.

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46

Tsutsumi, Shohei, Mitchell R. Rosen, and Roy S. Berns. "Spectral color management using interim connection spaces based on spectral decomposition." Color Research & Application 33, no. 4 (2008): 282–99. http://dx.doi.org/10.1002/col.20423.

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47

Tsutsumi, Shohei, Mitchell R. Rosen, and Roy S. Berns. "Spectral Color Management using Interim Connection Spaces based on Spectral Decomposition." Color and Imaging Conference 14, no. 1 (January 1, 2006): 246–51. http://dx.doi.org/10.2352/cic.2006.14.1.art00045.

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48

Kubrusly, C. S., and B. P. Duggal. "Weyl Spectral Identity and Biquasitriangularity." Proceedings of the Edinburgh Mathematical Society 59, no. 2 (October 29, 2015): 363–75. http://dx.doi.org/10.1017/s0013091515000267.

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AbstractLet A and B be operators acting on infinite-dimensional complex Banach spaces. We say that the Weyl spectral identity holds for the tensor product A⊗B if σw(A⊗B) = σw(A)·σ(B)∪σ(A)·σw(B), where σ(·) and σw(·) stand for the spectrum and the Weyl spectrum, respectively. Conditions on A and B for which the Weyl spectral identity holds are investigated. Especially, it is shown that if A and B are biquasitriangular (in particular, if the spectra of A and B have empty interior), then the Weyl spectral identity holds. It is also proved that if A and B are biquasitriangular, then the tensor product A ⊗ B is biquasitriangular.
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49

BEZHANISHVILI, GURAM, NICK BEZHANISHVILI, DAVID GABELAIA, and ALEXANDER KURZ. "Bitopological duality for distributive lattices and Heyting algebras." Mathematical Structures in Computer Science 20, no. 3 (January 18, 2010): 359–93. http://dx.doi.org/10.1017/s0960129509990302.

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We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces – the duals of Boolean algebras – and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important in the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, thereby providing two new alternatives to Esakia's duality.
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50

WALLET, JEAN-CHRISTOPHE. "CONNES DISTANCE BY EXAMPLES: HOMOTHETIC SPECTRAL METRIC SPACES." Reviews in Mathematical Physics 24, no. 09 (October 2012): 1250027. http://dx.doi.org/10.1142/s0129055x12500274.

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We study metric properties stemming from the Connes spectral distance on three types of non-compact non-commutative spaces which have received attention recently from various viewpoints in the physics literature. These are the non-commutative Moyal plane, a family of harmonic Moyal spectral triples for which the Dirac operator squares to the harmonic oscillator Hamiltonian and a family of spectral triples with the Dirac operator related to the Landau operator. We show that these triples are homothetic spectral metric spaces, having an infinite number of distinct pathwise connected components. The homothetic factors linking the distances are related to determinants of effective Clifford metrics. We obtain, as a by-product, new examples of explicit spectral distance formulas. The results are discussed in detail.
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