Symmetry and Spectral Invariance for Topologically Graded C*-Algebras and Partial Action Systems
arXiv:2108.09587
Abstract
A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any -algebra $\A$ is symmetric. We show that in each topologically graded -algebra over a rigidly symmetric group there is a -type symmetric Banach -algebra, which is inverse closed in the -algebra. This includes new general classes, as algebras admitting dual actions and partial crossed products. Results including convolution dominated kernels, inverse closedness with respect with ideals or weighted versions of the -decay are included. Various concrete examples are presented.
18 pages