scholarly journals Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture

2010 ◽  
Vol 207 (1) ◽  
pp. 29-70 ◽  
Author(s):  
Gregory Z. Arone ◽  
Kathryn Lesh
Keyword(s):  
Stable Rank ◽  
Whitehead Conjecture

DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

2021 ◽  
pp. 1-29
Author(s):  
ALEXANDER BRUDNYI
Keyword(s):  
Disjoint Union ◽  
A Priori ◽  
Holomorphic Functions ◽  
Stable Rank ◽  
Open Unit ◽  
Uniform Estimates ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Similar Approximation ◽  
Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

scholarly journals On the topological stable rank of non-selfadjoint operator algebras

2007 ◽  
Vol 341 (2) ◽  
pp. 239-253 ◽  
Author(s):  
K. R. Davidson ◽  
R. H. Levene ◽  
L. W. Marcoux ◽  
H. Radjavi
Keyword(s):  
Selfadjoint Operator ◽  
Operator Algebras ◽  
Stable Rank ◽  
Topological Stable Rank

scholarly journals The stable rank of pullbacks

2014 ◽  
Vol 410 ◽  
pp. 239-243 ◽  
Author(s):  
L.N. Vaserstein
Keyword(s):  
Stable Rank

scholarly journals Stable rank and real rank for some classes of group $C^\ast $-algebras

2005 ◽  
Vol 357 (6) ◽  
pp. 2165-2186 ◽  
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Stable Rank ◽  
Real Rank
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