Rapid Decay Subalgebras of C$^*$-Algebras

TL;DR

The paper presents a general method for constructing smooth subalgebras within C$^*$-algebras that support smooth calculus, demonstrated through various examples.

Contribution

It introduces a new scheme for creating smooth subalgebras of C$^*$-algebras, expanding the tools for analysis within operator algebras.

Findings

The scheme successfully constructs smooth subalgebras in multiple examples.

The subalgebras are closed under smooth calculus of self-adjoint elements.

The approach broadens the understanding of subalgebra structures in C$^*$-algebras.

Abstract

We introduce a general scheme of constructing smooth subalgebras of C$^*$-algebras that are closed under the smooth calculus of self-adjoint elements. We illustrate the scheme with a number of examples.