scholarly journals The C^*-algebra of compact perturbations of diagonal operators

2021 ◽  
pp. 59-84
Author(s):  
Esteban Andruchow ◽  
Eduardo Chiumiento ◽  
Alejandro Varela
Keyword(s):  
C Algebra ◽  
Diagonal Operators ◽  
Compact Perturbations

scholarly journals Compact actions on C*-algebras

1980 ◽  
Vol 21 (2) ◽  
pp. 143-149
Author(s):  
Charles A. Akemann ◽  
Steve Wright
Keyword(s):  
Banach Algebra ◽  
Compact Operator ◽  
Weakly Compact ◽  
C Algebra ◽  
C Algebras ◽  
Compact Perturbations

In Section 33 of [2], Bonsall and Duncan define an elementtof a Banach algebratoact compactlyonif the mapa→tatis a compact operator on. In this paper, the arguments and technique of [1] are used to study this question for C*-algebras (see also [10]). We determine the elementsbof a C*-algebrafor which the mapsa→ba,a→ab,a→ab+ba,a→babare compact (respectively weakly compact), determine the C*-algebras which are compact in the sense of Definition 9, of [2, p. 177] and give a characterization of the C*-automorphisms ofwhich are weakly compact perturbations of the identity.

scholarly journals Compact actions on C*-algebras

1980 ◽  
Vol 21 (1) ◽  
pp. 143-149 ◽  
Author(s):  
Charles A. Akemann ◽  
Steve Wright
Keyword(s):  
Banach Algebra ◽  
Compact Operator ◽  
Weakly Compact ◽  
C Algebra ◽  
C Algebras ◽  
Compact Perturbations

In Section 33 of [2], Bonsall and Duncan define an elementtof a Banach algebratoact compactlyonif the mapa→tatis a compact operator on. In this paper, the arguments and technique of [1] are used to study this question for C*-algebras (see also [10]). We determine the elementsbof a C*-algebrafor which the mapsa→ba,a→ab,a→ab+ba,a→babare compact (respectively weakly compact), determine the C*-algebras which are compact in the sense of Definition 9, of [2, p. 177] and give a characterization of the *-automorphisms ofwhich are weakly compact perturbations of the identity.

scholarly journals A non-diagonalizable pure state

2020 ◽  
Vol 117 (52) ◽  
pp. 33084-33089
Author(s):  
Piotr Koszmider
Keyword(s):  
Positive Solution ◽  
Pure State ◽  
Orthonormal Basis ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
C Algebra ◽  
Additional Hypothesis ◽  
Diagonal Operators

We construct a pure state on the C*-algebra B(ℓ2) of all bounded linear operators on ℓ2, which is not diagonalizable [i.e., it is not of the form limu⟨T(ek),ek⟩ for any orthonormal basis (ek)k∈N of ℓ2 and an ultrafilter u on N]. This constitutes a counterexample to Anderson’s conjecture without additional hypothesis and improves results of C. Akemann, N. Weaver, I. Farah, and I. Smythe who constructed such states making additional set-theoretic assumptions. It follows from results of J. Anderson and the positive solution to the Kadison–Singer problem due to A. Marcus, D. Spielman, and N. Srivastava that the restriction of our pure state to any atomic masa D((ek)k∈N) of diagonal operators with respect to an orthonormal basis (ek)k∈N is not multiplicative on D((ek)k∈N).

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

scholarly journals The Poincaré half-space of a C$^*$-algebra

2019 ◽  
Vol 35 (7) ◽  
pp. 2187-2219
Author(s):  
Esteban Andruchow ◽  
Gustavo Corach ◽  
Lázaro Recht
Keyword(s):  
Half Space ◽  
C Algebra

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

scholarly journals Measuring Multijet Structure of Hadronic Energy Flow or, What is a jet?

1997 ◽  
Vol 12 (30) ◽  
pp. 5411-5529 ◽  
Author(s):  
Fyodor V. Tkachov
Keyword(s):  
Energy Flow ◽  
Mass Spectra ◽  
Analytical Control ◽  
Final States ◽  
C Algebra ◽  
Approximation Errors ◽  
Basic Class ◽  
Jet Algorithms ◽  
Hadronic Energy ◽  
Optimal Recombination

Ambiguities of jet algorithms are reinterpreted as instability wrt small variations of input. Optimal stability occurs for observables possessing property of calorimetric continuity (C-continuity) predetermined by kinematical structure of calorimetric detectors. The so-called C-correlators form a basic class of such observables and fit naturally into QFT framework, allowing systematic theoretical studies. A few rules generate other C-continuous observables. The resulting C-algebra correctly quantifies any feature of multijet structure such as the "number of jets" and mass spectra of "multijet substates." The new observables are physically equivalent to traditional ones but can be computed from final states bypassing jet algorithms which reemerge as a tool of approximate computation of C-observables from data with all ambiguities under analytical control and an optimal recombination criterion minimizing approximation errors.

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

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