Hyperrigid generators in C∗ -algebras

Article Type

Research Article

Publication Title

Journal of Analysis

Abstract

In this article, we show that, if S∈ B(H) is irreducible and essential unitary, then { S, SS∗} is a hyperrigid generator for the unital C∗-algebra T generated by S. We prove that, if T is an operator in B(H) that generates a unital C∗-algebra A then { T, T∗T, TT∗} is a hyperrigid generator for A. As a corollary it follows that, if T∈ B(H) is normal then { T, TT∗} is hyperrigid generator for the unital C∗-algebra generated by T and if T∈ B(H) is unitary then { T} is hyperrigid generator for the C∗-algebra generated by T. We show that if V∈ B(H) is an isometry (not unitary) that generates the C∗-algebra A then the minimal generating set { V} is not hyperrigid for A.

First Page

791

Last Page

797

DOI

10.1007/s41478-019-00199-9

Publication Date

9-1-2020

Comments

Open Access, Green

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