Vol. 110, No. 2, 1984

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The range of convolution operators

Robert A. Bekes

Vol. 110 (1984), No. 2, 257–271
Abstract

Subject to certain restrictions, convolving on the right by a fixed function defines a bounded linear operator between spaces of measures or functions over a locally compact group. For non-compact groups we show that when the range and domain are different, such operators rarely have closed range. Applications of these results are made to representation theory for locally compact groups. We also prove a correspondence theorem for strictly cyclic vectors for Banach algebras and those for certain closed left ideals.

Mathematical Subject Classification 2000
Primary: 43A15
Secondary: 43A22
Milestones
Received: 18 June 1981
Revised: 25 May 1982
Published: 1 February 1984
Authors
Robert A. Bekes