New York Journal of Mathematics
Volume 30 (2024), 398-421


Justin R. Peters

Singly generated radical operator algebras

view    print

Published: March 8, 2024.
Keywords: operator algebra, C*-cover, completely isometric isomorphism, gauge automorphism, wieghted shift operator, Volterra integral operator.
Subject [2010]: Primary: 47L80; Secondary: 46J45.

We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted shift algebra, the existence of a gauge action allows us to apply Fourier analysis to study the ideals of the algebra. In the case of the Volterra operator algebra, there is no gauge action, and other methods are needed to study the norm structure and the ideals.


The author would like to thank Chris Phillips for his comments on an earlier version of this paper.

Author information

Justin R. Peters
Department of Mathematics
Iowa State University
Ames, Iowa 50011, USA