Similarity implies homotopy of idempotents in Banach algebras of stable rank one

2007 ◽  
Vol 88 (3) ◽  
pp. 235-238
Author(s):  
Julien Giol
Keyword(s):  
Banach Algebras ◽  
Stable Rank ◽  
Rank One

scholarly journals STABLE RANK FOR INCLUSIONS OF C*-ALGEBRAS

2008 ◽  
Vol 19 (09) ◽  
pp. 1011-1020 ◽  
Author(s):  
HIROYUKI OSAKA
Keyword(s):  
Finite Groups ◽  
Stable Rank ◽  
C Algebra ◽  
C Algebras ◽  
Rank One ◽  
Common Unit ◽  
Topological Stable Rank

When a unital C*-algebra A has topological stable rank one (write tsr (A) = 1), we know that tsr (pAp) = 1 for a non-zero projection p ∈ A. When, however, tsr (A) ≥ 2, it is generally false. We prove that if a unital C*-algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and sup p ∈ P(D) tsr (pAp) < ∞, then tsr (A) ≤ 2. As an application let A be a simple unital C*-algebra with tsr (A) = 1 and Property (SP), [Formula: see text] finite groups, αk actions from Gk to Aut ((⋯((A × α1 G1) ×α2 G2)⋯) ×αk-1 Gk-1). (G0 = {1}). Then [Formula: see text]

scholarly journals CANCELLATION DOES NOT IMPLY STABLE RANK ONE

2006 ◽  
Vol 38 (06) ◽  
pp. 1005-1008 ◽  
Author(s):  
ANDREW S. TOMS
Keyword(s):  
Stable Rank ◽  
Rank One

scholarly journals Continuous selections and stable rank of Banach algebras

1992 ◽  
Vol 43 (3) ◽  
pp. 237-248 ◽  
Author(s):  
Gustavo Corach ◽  
Fernando Daniel Suárez
Keyword(s):  
Banach Algebras ◽  
Stable Rank ◽  
Continuous Selections

Ideal Structure of Multiplier Algebras of Simple C*-algebras With Real Rank Zero

2001 ◽  
Vol 53 (3) ◽  
pp. 592-630 ◽  
Author(s):  
Francesc Perera
Keyword(s):  
Stable Rank ◽  
Real Rank ◽  
Ideal Structure ◽  
Real Rank Zero ◽  
Von Neumann ◽  
Rank Zero ◽  
Rank One ◽  
A Chain ◽  
Multiplier Algebras ◽  
The Ideal

AbstractWe give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of σ-unital simple C*-algebras A with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of themultiplier algebra , is therefore analyzed. In important cases it is shown that, if A has finite scale then the quotient of modulo any closed ideal I that properly contains A has stable rank one. The intricacy of the ideal structure of is reflected in the fact that can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.

scholarly journals Extremally rich C*-crossed products and the cancellation property

1998 ◽  
Vol 64 (3) ◽  
pp. 285-301 ◽  
Author(s):  
Ja A Jeong ◽  
Hiroyuki Osaka
Keyword(s):  
Finite Abelian Group ◽  
Extreme Points ◽  
Stable Rank ◽  
Crossed Product ◽  
Closed Unit Ball ◽  
Crossed Products ◽  
Cancellation Property ◽  
Rank One ◽  
Invertible Elements ◽  
Unital Simple

AbstractA unital C*-algebra A is called extremally rich if the set of quasi-invertible elements A-1 ex (A)A-1 (= A-1q) is dense in A, where ex(A) is the set of extreme points in the closed unit ball A1 of A. In [7, 8] Brown and Pedersen introduced this notion and showed that A is extremally rich if and only if conv(ex(A)) = A1. Any unital simple C*-algebra with extremal richness is either purely infinite or has stable rank one (sr(A) = 1). In this note we investigate the extremal richness of C*-crossed products of extremally rich C*-algebras by finite groups. It is shown that if A is purely infinite simple and unital then A xα, G is extremally rich for any finite group G. But this is not true in general when G is an infinite discrete group. If A is simple with sr(A) =, and has the SP-property, then it is shown that any crossed product A xαG by a finite abelian group G has cancellation. Moreover if this crossed product has real rank zero, it has stable rank one and hence is extremally rich.

Rank one elements of Banach algebras

Mathematika ◽  
1977 ◽  
Vol 24 (2) ◽  
pp. 178-181 ◽  
Author(s):  
J. A. Erdos ◽  
S. Giotopoulos ◽  
M. S. Lambrou
Keyword(s):  
Banach Algebras ◽  
Rank One

THE CONNECTED STABLE RANK FOR BANACH *-ALGEBRAS INVOLVING ISOMETRIES

2010 ◽  
Vol 03 (01) ◽  
pp. 185-191
Author(s):  
Takahiro Sudo
Keyword(s):  
Banach Algebras ◽  
Stable Rank

It is shown that the connected stable rank of a unital Banach *-algebra containing two isometries with orthogonal ranges is infinity. Several consequences as its applications and variations are also obtained.

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