Vol. 80, No. 1, 1979

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Compact operators of the form uCφ

Herbert Meyer Kamowitz

Vol. 80 (1979), No. 1, 205–211
Abstract

If A is the disc algebra, the uniform algebra of functions analytic on the open unit disc D and continuous on its closure, and if u,φ A with φ1, then the operator uCφ is defined on A by uCφ : f(z) u(z)f(φ(z)). In this note we characterize compact operators of this form and determine their spectra.

Mathematical Subject Classification 2000
Primary: 47B38
Secondary: 47B05
Milestones
Received: 1 December 1977
Revised: 5 May 1978
Published: 1 January 1979
Authors
Herbert Meyer Kamowitz