On the topological stable rank of non-selfadjoint operator algebras

Details On the topological stable rank of non-selfadjoint operator algebras On the topological stable rank of non-selfadjoint operator algebras

2007-06-16

arxiv.org/abs/0706.2447v1

Mathematics

Operator Algebras

14 pages

Scientific paper

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 free semigroup algebras as well.

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