scholarly journals Invertibility-preserving maps ofC∗-algebras with real rank zero

2005 ◽  
Vol 2005 (6) ◽  
pp. 685-689 ◽  
Author(s):  
Istvan Kovacs
Keyword(s):  
Banach Algebras ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Linear Map ◽  
Linear Bijection ◽  
Jordan Isomorphism ◽  
Invertible Elements

In 1996, Harris and Kadison posed the following problem: show that a linear bijection betweenC∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that ifAandBare semisimple Banach algebras andΦ:A→Bis a linear map ontoBthat preserves the spectrum of elements, thenΦis a Jordan isomorphism if eitherAorBis aC∗-algebra of real rank zero. We also generalize a theorem of Russo.

scholarly journals A Complete Invariant forADAlgebras with Real Rank Zero and Bounded Torsion inK1

1996 ◽  
Vol 139 (2) ◽  
pp. 325-348 ◽  
Author(s):  
Søren Eilers
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero

scholarly journals Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

2014 ◽  
Vol 14 (3) ◽  
pp. 570-613 ◽  
Author(s):  
Sara E. Arklint ◽  
Rasmus Bentmann ◽  
Takeshi Katsura
Keyword(s):  
Primitive Ideal ◽  
Ideal Space ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
K Theory

AbstractWe show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces—including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz–Krieger algebras whose primitive ideal space is an accordion space.

scholarly journals The real rank zero property of crossed product

2006 ◽  
Vol 134 (10) ◽  
pp. 3015-3024 ◽  
Author(s):  
Xiaochun Fang
Keyword(s):  
Crossed Product ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
The Real

scholarly journals Linear orthogonality preservers of Hilbert $C^{*}$-modules over $C^{*}$-algebras with real rank zero

2012 ◽  
Vol 140 (9) ◽  
pp. 3151-3160 ◽  
Author(s):  
Chi-Wai Leung ◽  
Chi-Keung Ng ◽  
Ngai-Ching Wong
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Orthogonality Preservers

Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in

2011 ◽  
Vol 54 (1) ◽  
pp. 141-146
Author(s):  
Sang Og Kim ◽  
Choonkil Park
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Calkin Algebra ◽  
C Algebras ◽  
Linear Maps

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.

scholarly journals Type I $C^*$-algebras of real rank zero

1997 ◽  
Vol 125 (9) ◽  
pp. 2671-2676
Author(s):  
Huaxin Lin
Keyword(s):  
Type I ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras

scholarly journals On the classification of C*-algebras of real rank zero, III: The infinite case

1998 ◽  
pp. 11-72 ◽  
Author(s):  
Ola Bratteli ◽  
George Elliott ◽  
David Evans ◽  
Akitaka Kishimoto
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Infinite Case

Intrinsic Covering Dimension for Nuclear C*-Algebras with Real Rank Zero

2016 ◽  
Vol 86 (3) ◽  
pp. 301-319
Author(s):  
Nicola Watson
Keyword(s):  
Real Rank ◽  
Covering Dimension ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras

scholarly journals Kirchberg X-algebras with real rank zero and intermediate cancellation

2014 ◽  
Vol 8 (4) ◽  
pp. 1061-1081 ◽  
Author(s):  
Rasmus Bentmann
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero

C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups

1996 ◽  
Vol 39 (4) ◽  
pp. 429-437 ◽  
Author(s):  
K. R. Goodearl
Keyword(s):  
Real Rank ◽  
Riesz Decomposition Property ◽  
Real Rank Zero ◽  
Decomposition Property ◽  
Rank Zero ◽  
C Algebras ◽  
Finite Dimensional ◽  
Riesz Decomposition ◽  
Stably Finite ◽  
The Riesz Decomposition Property

AbstractExamples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.

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