Reductivity in C^∗-algebras and essentially reductive operators

Robert Laurens Moore

Vol. 74 (1978), No. 2, 419–428

DOI: 10.2140/pjm.1978.74.419

Abstract

Reductivity is defined in the context of C^∗-algebras other than the algebra of bounded operators on Hilbert space, and several examples are given. Essentially reductive operators are defined as operators whose images are reductive in the Calkin algebra. It is shown that every essentially reductive operator must be a compact perturbation of a reductive normal operator.

Mathematical Subject Classification 2000

Primary: 46L05

Secondary: 47C10

Milestones

Received: 14 September 1976

Published: 1 February 1978