Rapid Decay Subalgebras of C$^*$-Algebras
Shelley Hebert, Slawomir Klimek, Matt McBride

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.
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