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Journal articles on the topic 'Calkin algebra'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

GHASEMI, SAEED. "SAW*-ALGEBRAS ARE ESSENTIALLY NON-FACTORIZABLE." Glasgow Mathematical Journal 57, no. 1 (August 26, 2014): 1–5. http://dx.doi.org/10.1017/s0017089514000093.

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AbstractIn this paper, we solve a question of Simon Wassermann, whether the Calkin algebra can be written as a C*-tensor product of two infinite dimensional C*-algebras. More generally, we show that there is no surjective *-homomorphism from a SAW*-algebra onto C*-tensor product of two infinite dimensional C*-algebras.

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2

Lin, Pei-Kee. "A counterexample of hermitian liftings." Proceedings of the Edinburgh Mathematical Society 32, no. 2 (June 1989): 255–59. http://dx.doi.org/10.1017/s0013091500028650.

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Let X be a complex Banach space, and let and denote respectively the algebras of bounded and compact operators on X. The quotient algebra is called the Calkin algebra associated with X. It is known that both and are complex Banach algebras with unit e. For such unital Banach algebras B, setand define the numerical range of x ∈ B asx is said to be hermitian if W(x)⊆R. It is known thatFact 1. ([4 vol. I, p. 46]) x is hermitian if and only if ‖eiαx‖ = (or ≦)1 for all α ∈ R, where ex is defined by

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3

Zhu, Sen, and YouQing Ji. "Similarity orbits in the Calkin algebra." Science China Mathematics 54, no. 6 (May 2011): 1225–32. http://dx.doi.org/10.1007/s11425-011-4207-8.

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4

Farah, Ilijas, Ilan Hirshberg, and Alessandro Vignati. "The Calkin algebra is ℵ1-universal." Israel Journal of Mathematics 237, no. 1 (May 14, 2020): 287–309. http://dx.doi.org/10.1007/s11856-020-2007-y.

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5

Hadwin, Don. "Maximal nests in the Calkin algebra." Proceedings of the American Mathematical Society 126, no. 4 (1998): 1109–13. http://dx.doi.org/10.1090/s0002-9939-98-04233-6.

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6

Phillips, N. Christopher, and Nik Weaver. "The Calkin algebra has outer automorphisms." Duke Mathematical Journal 139, no. 1 (July 2007): 185–202. http://dx.doi.org/10.1215/s0012-7094-07-13915-2.

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7

Kim, Sang Og, and Choonkil Park. "Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in." Canadian Mathematical Bulletin 54, no. 1 (March 1, 2011): 141–46. http://dx.doi.org/10.4153/cmb-2010-087-x.

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AbstractFor C*-algebras of real rank zero, we describe linear maps ϕ on that are surjective up to ideals , and π(A) is invertible in if and only if π(ϕ(A)) is invertible in , where A ∈ and π : → is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra.

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8

Weaver, Nik. "Set Theory and C*-Algebras." Bulletin of Symbolic Logic 13, no. 1 (March 2007): 1–20. http://dx.doi.org/10.2178/bsl/1174668215.

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9

Derezinski, Jan. "N-Body Observables in the Calkin Algebra." Transactions of the American Mathematical Society 332, no. 2 (August 1992): 571. http://dx.doi.org/10.2307/2154184.

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10

Astala, Kari, and Hans-Olav Tylli. "On Semifredholm Operators and the Calkin Algebra." Journal of the London Mathematical Society s2-34, no. 3 (December 1986): 541–51. http://dx.doi.org/10.1112/jlms/s2-34.3.541.

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11

Dereziński, Jan. "$N$-body observables in the Calkin algebra." Transactions of the American Mathematical Society 332, no. 2 (February 1, 1992): 571–82. http://dx.doi.org/10.1090/s0002-9947-1992-1117217-3.

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12

Farah, Ilijas, and Ilan Hirshberg. "The Calkin algebra is not countably homogeneous." Proceedings of the American Mathematical Society 144, no. 12 (May 23, 2016): 5351–57. http://dx.doi.org/10.1090/proc/13137.

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13

Zhang, Shuang. "On the Structure of Projections and Ideals of Corona Algebras." Canadian Journal of Mathematics 41, no. 4 (August 1, 1989): 721–42. http://dx.doi.org/10.4153/cjm-1989-033-4.

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If K is the set of all compact bounded operators and L(H) is the set of all bounded operators on a separable Hilbert space H, then L(H) is the multiplier algebra of K. In general we denote the multiplier algebra of a C*-algebra A by M(A). For more information about M(A), readers are referred to the articles [1], [3],[7], [9], [14], [18],[20], [23], [26], [27], among others. It is well known that in the Calkin algebra L(H)/K every nonzero projection is infinite. If we assume that A is a-unital (nonunital) and regard the corona algebra M(A)/A as a generalized case of the Calkin algebra, is every nonzero projection in M(A)/A still infinite? Another basic question can be raised: How does the (closed) ideal structure of A relate to the (closed) ideal structure of M(A)/A?In the first part of this note (Sections 1 and 2) we shall give an affirmative answer for the first question if A is a simple a-unital (nonunital) C*-algebra with FS.

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14

Matthew Bice, Tristan. "Filters in C*-Algebras." Canadian Journal of Mathematics 65, no. 3 (June 1, 2013): 485–509. http://dx.doi.org/10.4153/cjm-2011-095-4.

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AbstractIn this paper we analyze states on C*-algebras and their relationship to filter-like structures of projections and positive elements in the unit ball. After developing the basic theory we use this to investigate the Kadison–Singer conjecture, proving its equivalence to an apparently quite weak paving conjecture and the existence of unique maximal centred extensions of projections coming from ultrafilters on the natural numbers. We then prove that Reid's positive answer to this for q-points in fact also holds for rapid p-points, and that maximal centred filters are obtained in this case. We then show that consistently, such maximal centred filters do not exist at all meaning that, for every pure state on the Calkin algebra, there exists a pair of projections on which the state is 1, even though the state is bounded strictly below 1 for projections below this pair. Next, we investigate towers, using cardinal invariant equalities to construct towers on the natural numbers that do and do not remain towers when canonically embedded into the Calkin algebra. Finally, we show that consistently, all towers on the natural numbers remain towers under this embedding.

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15

Berkani, Mohammed, and Snezana Zivkovic-Zlatanovic. "Pseudo-B-Fredholm operators, poles of the resolvent and mean convergence in the calkin algebra." Filomat 33, no. 11 (2019): 3351–59. http://dx.doi.org/10.2298/fil1911351b.

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We define here a pseudo B-Fredholm operator as an operator such that 0 is isolated in its essential spectrum, then we prove that an operator T is pseudo-B-Fredholm if and only if T = R + F where R is a Riesz operator and F is a B-Fredholm operator such that the commutator [R,F] is compact. Moreover, we prove that 0 is a pole of the resolvent of an operator T in the Calkin algebra if and only if T = K + F, where K is a power compact operator and F is a B-Fredholm operator, such that the commutator [K,F] is compact. As an application, we characterize the mean convergence in the Calkin algebra.

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16

Han, Sandie, Ariane M. Masuda, Satyanand Singh, and Johann Thiel. "The (u,v)-Calkin–Wilf forest." International Journal of Number Theory 12, no. 05 (May 10, 2016): 1311–28. http://dx.doi.org/10.1142/s1793042116500809.

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In this paper, we consider a refinement, due to Nathanson, of the Calkin–Wilf tree. In particular, we study the properties of such trees associated with the matrices [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative integers. We extend several known results of the original Calkin–Wilf tree, including the symmetry, numerator-denominator, and successor formulas, to this new setting. Additionally, we study the ancestry of a rational number appearing in a generalized Calkin–Wilf tree.

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17

Farah, Ilijas. "All automorphisms of the Calkin algebra are inner." Annals of Mathematics 173, no. 2 (March 1, 2011): 619–61. http://dx.doi.org/10.4007/annals.2011.173.2.1.

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18

Bel Hadj Fredj, O. "On the poles of the resolvent in Calkin algebra." Proceedings of the American Mathematical Society 135, no. 07 (July 1, 2007): 2229–35. http://dx.doi.org/10.1090/s0002-9939-07-08733-3.

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19

Kriete, Thomas, and Jennifer Moorhouse. "Linear relations in the Calkin algebra for composition operators." Transactions of the American Mathematical Society 359, no. 6 (January 4, 2007): 2915–44. http://dx.doi.org/10.1090/s0002-9947-07-04166-9.

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20

Gravner, Janko. "A note on elementary operators on the Calkin algebra." Proceedings of the American Mathematical Society 97, no. 1 (January 1, 1986): 79. http://dx.doi.org/10.1090/s0002-9939-1986-0831392-x.

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21

Castro-González, N., and J. Y. Vélez-Cerrada. "Elements of rings and Banach algebras with related spectral idempotents." Journal of the Australian Mathematical Society 80, no. 3 (June 2006): 383–96. http://dx.doi.org/10.1017/s1446788700014099.

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AbstractLet aπ denote the spectral idempotent of a generalized Drazin invertible element a of a ring. We characterize elements b such that 1 − (bπ − aπ)2 is invertible. We also apply this result in rings with involution to obtain a characterization of the perturbation of EP elements. In Banach algebras we obtain a characterization in terms of matrix representations and derive error bounds for the perturbation of the Drazin Inverse. This work extends recent results for matrices given by the same authors to the setting of rings and Banach algebras. Finally, we characterize generalized Drazin invertible operators A, B ∈ (X) such that pr(Bπ) = pr(Aπ + S), where pr is the natural homomorphism of (X) onto the Calkin algebra and S ∈(X) is given.2000 Mathematics subject classification: primary 16A32, 16A28, 15A09.

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22

Lee, Hong-Youl. "ON A TOPOLOGICAL DIVISOR OF ZERO IN THE CALKIN ALGEBRA." Bulletin of the Korean Mathematical Society 43, no. 3 (August 1, 2006): 653–55. http://dx.doi.org/10.4134/bkms.2006.43.3.653.

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23

Wofsey, Eric. "$P(\omega)/{\rm fin}$ and projections in the Calkin algebra." Proceedings of the American Mathematical Society 136, no. 02 (November 6, 2007): 719–26. http://dx.doi.org/10.1090/s0002-9939-07-09093-4.

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24

Zamora-Aviles, Beatriz. "Gaps in the poset of projections in the Calkin algebra." Israel Journal of Mathematics 202, no. 1 (April 3, 2014): 105–15. http://dx.doi.org/10.1007/s11856-014-1057-4.

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25

Andruchow, Esteban. "A note on geodesics of projections in the Calkin algebra." Archiv der Mathematik 115, no. 5 (August 11, 2020): 545–53. http://dx.doi.org/10.1007/s00013-020-01509-5.

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26

Roch, Steffen, and Bernd Silbermann. "The Calkin image of algebras of singular integral operators." Integral Equations and Operator Theory 12, no. 6 (November 1989): 855–97. http://dx.doi.org/10.1007/bf01196881.

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27

Xia, Jingbo. "A double commutant relation in the Calkin algebra on the Bergman space." Journal of Functional Analysis 274, no. 6 (March 2018): 1631–56. http://dx.doi.org/10.1016/j.jfa.2017.11.004.

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28

Laustsen, Niels Jakob, and Richard Skillicorn. "Extensions and the weak Calkin algebra of Read’s Banach space admitting discontinuous derivations." Studia Mathematica 236, no. 1 (2017): 51–62. http://dx.doi.org/10.4064/sm8554-9-2016.

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29

Xia, Jingbo. "Coincidence of essential commutant and the double commutant relation in the Calkin algebra." Journal of Functional Analysis 197, no. 1 (January 2003): 140–50. http://dx.doi.org/10.1016/s0022-1236(02)00034-4.

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30

Xia, Jingbo. "Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant." Canadian Mathematical Bulletin 45, no. 2 (June 1, 2002): 309–18. http://dx.doi.org/10.4153/cmb-2002-034-9.

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AbstractA well-known theorem of Sarason [11] asserts that if [Tf, Th] is compact for every h ∈ H∞, then f ∈ H∞ + C(T). Using local analysis in the full Toeplitz algebra τ = τ(L∞), we show that the membership f ∈ H∞ + C(T) can be inferred from the compactness of a much smaller collection of commutators [Tf, Th]. Using this strengthened result and a theorem of Davidson [2], we construct a proper C*-subalgebra τ(L)) of τ which has the same essential commutant as that of τ. Thus the image of τ(ℒ) in the Calkin algebra does not satisfy the double commutant relation [12], [1]. We will also show that no separable subalgebra Ѕ of τ is capable of conferring the membership f ∈ H∞ + C(T) through the compactness of the commutators {[Tf, S] : S ∈ Ѕ}.

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31

Burnap, Charles, and Alan Lambert. "Proximity and similarity of operators II." Glasgow Mathematical Journal 32, no. 2 (May 1990): 205–13. http://dx.doi.org/10.1017/s001708950000923x.

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In this paper we continue the examination of the question of similarity of operators A and B begun in reference [3]. In that article, a similarity result was obtained based on a measure of closeness, or proximity, of the uniformly continuous semigroups etA and etB, t>0. The operators considered were elements of ℬ(ℋ), the algebra of bounded operators on a Hilbert space ℬWe now wish to relax this requirement and replace ℬ(ℋ) by a complex Banach algebra ℬ with unit I. In Section 2 we give a necessary condition for the similarity of A, B ∈ ℋ. We then give a condition sufficient to guarantee A and B are approximately similar (as defined in reference [5]). In Section 3 we restrict our attention to the case where ℋ = ℋ(ℋ). There we give a condition which guarantees A, B ∈ ℋ(ℋ) are intertwined by a Fredholm operator. This leads naturally into a discussion of proximity-similarity in the Calkin algebra si. This is the subject of Section 4. Following reference [7] we define a metric p on N(ℋ), the normal elements of ℋ We show (N(ℋ), p) is a complete metric space and that the unitary orbit of ℋ (N(ℋ) p)is the p-connected component of a in N (ℋ).

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32

Schimmerling, Ernest. "Ilijas Farah. All automorphisms of the Calkin algebra are inner. Annals of Mathematics, vol. 173 (2010), no. 2, pp. 619–661." Bulletin of Symbolic Logic 17, no. 3 (September 2011): 467–70. http://dx.doi.org/10.1017/s1079898600000482.

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33

Mathieu, Martin. "Elementary Operators on Calkin Algebras." Irish Mathematical Society Bulletin 0046 (2001): 33–42. http://dx.doi.org/10.33232/bims.0046.33.42.

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34

Farah, Ilijas, Paul McKenney, and Ernest Schimmerling. "Some Calkin algebras have outer automorphisms." Archive for Mathematical Logic 52, no. 5-6 (April 6, 2013): 517–24. http://dx.doi.org/10.1007/s00153-013-0329-8.

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35

Farah, Ilijas. "All automorphisms of all Calkin algebras." Mathematical Research Letters 18, no. 3 (2011): 489–503. http://dx.doi.org/10.4310/mrl.2011.v18.n3.a9.

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36

Skillicorn, Richard. "The uniqueness-of-norm problem for Calkin algebras." Mathematical Proceedings of the Royal Irish Academy 115A, no. 2 (2015): 1–8. http://dx.doi.org/10.1353/mpr.2015.0005.

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37

Meyer, Michael J. "On a Topological Property of certain Calkin Algebras." Bulletin of the London Mathematical Society 24, no. 6 (November 1992): 591–98. http://dx.doi.org/10.1112/blms/24.6.591.

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38

Boedihardjo, March T., and William B. Johnson. "On mean ergodic convergence in the Calkin algebras." Proceedings of the American Mathematical Society 143, no. 6 (January 21, 2015): 2451–57. http://dx.doi.org/10.1090/s0002-9939-2015-12432-x.

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39

Richard Skillicorn. "The uniqueness-of-norm problem for Calkin algebras." Mathematical Proceedings of the Royal Irish Academy 115A, no. 2 (2015): 1. http://dx.doi.org/10.3318/pria.2015.115.14.

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40

Hadwin, D. "A Reflexivity Theorem for Subspaces of Calkin Algebras." Journal of Functional Analysis 123, no. 1 (July 1994): 1–11. http://dx.doi.org/10.1006/jfan.1994.1080.

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41

Horváth, Bence, and Tomasz Kania. "Unital Banach algebras not isomorphic to Calkin algebras of separable Banach spaces." Proceedings of the American Mathematical Society 149, no. 11 (August 6, 2021): 4781–87. http://dx.doi.org/10.1090/proc/15589.

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42

Schmüdgen, Konrad. "Topological Realizations of Calkin Algebras on Frechet Domains of Unbounded Operator Algebras." Zeitschrift für Analysis und ihre Anwendungen 5, no. 6 (1986): 481–90. http://dx.doi.org/10.4171/zaa/217.

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43

González, Manuel, and José M. Herrera. "Calkin algebras for Banach spaces with finitely decomposable quotients." Studia Mathematica 157, no. 3 (2003): 279–93. http://dx.doi.org/10.4064/sm157-3-3.

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44

Saksman, Eero, and Hans-Olav Tylli. "Rigidity of commutators and elementary operators on Calkin algebras." Israel Journal of Mathematics 108, no. 1 (December 1998): 217–36. http://dx.doi.org/10.1007/bf02783049.

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45

Motakis, Pavlos, Daniele Puglisi, and Andreas Tolias. "Algebras of Diagonal Operators of the Form Scalar-Plus-Compact Are Calkin Algebras." Michigan Mathematical Journal 69, no. 1 (March 2020): 97–152. http://dx.doi.org/10.1307/mmj/1574845272.

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46

Hofmann, Gerald, and Frank Löffler. "On Inner Characterizations of Aõ-Algebras and some Applications to Calkin Algebras and Symmetric Tensor-Algebras." Mathematische Nachrichten 148, no. 1 (1990): 247–70. http://dx.doi.org/10.1002/mana.3211480116.

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47

Motakis, Pavlos, Daniele Puglisi, and Despoina Zisimopoulou. "A hierarchy of Banach spaces with C(K) Calkin algebras." Indiana University Mathematics Journal 65, no. 1 (2016): 39–67. http://dx.doi.org/10.1512/iumj.2016.65.5756.

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48

ADÁMEK, JIŘÍ, STEFAN MILIUS, and JIŘÍ VELEBIL. "Iterative reflections of monads." Mathematical Structures in Computer Science 20, no. 3 (February 4, 2010): 419–52. http://dx.doi.org/10.1017/s0960129509990326.

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Iterative monads were introduced by Calvin Elgot in the 1970's and are those ideal monads in which every guarded system of recursive equations has a unique solution. We prove that every ideal monad has an iterative reflection, that is, an embedding into an iterative monad with the expected universal property. We also introduce the concept of iterativity for algebras for the monad , following in the footsteps of Evelyn Nelson and Jerzy Tiuryn, and prove that is iterative if and only if all free algebras for are iterative algebras.

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49

Kürsten, Klaus-Detlef, and Michael Milde. "Calkin Representations of Unbounded Operator Algebras Acting on Non-Separable Domains." Mathematische Nachrichten 154, no. 1 (1991): 285–300. http://dx.doi.org/10.1002/mana.19911540124.

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50

Farah, Ilijas, Georgios Katsimpas, and Andrea Vaccaro. "Embedding ${\mathrm{C}}^\ast $-Algebras Into the Calkin Algebra." International Mathematics Research Notices, April 3, 2019. http://dx.doi.org/10.1093/imrn/rnz058.

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