On Homotopy Invariants of Tensor Products of Banach Algebras

TL;DR

This paper extends existing results on the homotopy types of invertible elements and idempotents in the tensor product of complex Banach algebras, providing new insights and specific examples.

Contribution

It generalizes previous work by Davie and Raeburn on homotopy invariants in tensor products of Banach algebras, introducing broader applicability.

Findings

Homotopy types of invertible elements characterized

Homotopy types of idempotents described

Examples illustrating the theoretical results

Abstract

We generalize results of Davie and Raeburn describing homotopy types of the group of invertible elements and of the set of idempotents of the projective tensor product of complex unital Banach algebras. We illustrate our results by specific examples.