JB*-Algebras of Topological Stable Rank 1

Topological 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...

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...

Automatic Continuity of Higher Derivations on JB*-Algebras

On 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...

On the stable rank and reducibility in algebras of real symmetric func- tions

Let AR(D) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that AR(D) has Bass and topological stable ranks equal to 2, which settles the conjecture made by Brett Wick in [18]. We also give a necessary and sufficient condition for reducibility in some real algebras of functions on symmetric domains with holes, which is a generalization of the m...