Vol. 74, No. 2, 1978

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Reductivity in Cāˆ—-algebras and essentially reductive operators

Robert Laurens Moore

Vol. 74 (1978), No. 2, 419ā€“428
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
Authors
Robert Laurens Moore