Symmetry and Spectral Invariance for Topologically Graded C*-Algebras and Partial Action Systems

Diego Jaure; Marius Mantoiu

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arXiv · 2108.09587

Symmetry and Spectral Invariance for Topologically Graded C*-Algebras and Partial Action Systems

Diego Jaure·Marius Mantoiu

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Abstract

A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly symmetric group there is a $\ell^1$-type symmetric Banach $^*$-algebra, which is inverse closed in the $C^*$-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 $\ell^1$-decay are included. Various concrete examples are presented.

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BibTeX RIS

Diego Jaure, Marius Mantoiu. 2021-08-21. Symmetry and Spectral Invariance for Topologically Graded C*-Algebras and Partial Action Systems. https://arxiv.org/abs/2108.09587

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