منابع مشابه
Topological stable rank of nest algebras
We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or in...
متن کاملJB*-Algebras of Topological Stable Rank 1
In 1976, Kaplansky introduced the class JB∗-algebras which includes all C∗-algebras as a proper subclass. The notion of topological stable rank 1 for C∗-algebras was originally introduced by M. A. Rieffel and was extensively studied by various authors. In this paper, we extend this notion to general JB∗-algebras. We show that the complex spin factors are of tsr 1 providing an example of special...
متن کاملTopological Stable Rank of Inclusions of Unital C*-algebras
Let 1 ∈ A ⊂ B be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of B (= tsr(B)) when A has topological stable rank one. We show that tsr(B) ≤ 2 when A is a tsr boundedly divisible algebra, in particular, A is a C*-minimal tensor product UHF ⊗ D with tsr(D) = 1. When G is a finite group and α is an action of G on UHF, we know that a cr...
متن کاملOn the Topological Stable Rank of Non-selfadjoint Operator Algebras
We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras, both the left and right topological stable ranks are infinite. We extend this latter result to Popescu’s non-commutative disc algebras and to fr...
متن کامل-algebras of Tracial Topological Rank One *
We give a classification theorem for unital separable nuclear simple C∗-algebras with tracial rank no more than one. Let A and B be two unital separable simple nuclear C∗-algebras with TR(A), TR(B) ≤ 1 which satisfy the universal coefficient theorem. We show that A ∼= B if and only if there is an order and unit preserving isomorphism γ = (γ0, γ1, γ2) : (K0(A),K0(A)+, [1A],K1(A), T (A)) ∼= (K0(B...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2008
ISSN: 0024-6115
DOI: 10.1112/plms/pdn048