Compact operators of the form uC_φ

Herbert Meyer Kamowitz

Vol. 80 (1979), No. 1, 205–211

DOI: 10.2140/pjm.1979.80.205

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 ∥φ∥≦ 1, then the operator uC_φ is defined on A by uC_φ : 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