Isometric multipliers

Stephen Parrott

Vol. 25 (1968), No. 1, 159–166

DOI: 10.2140/pjm.1968.25.159

Abstract

Let G be a locally compact group with right Haar measure. A left multiplier on L^p(G) is a bounded operator which commutes with all the operators induced by left translations. The main theorem of this paper states that every isometric left multiplier on L^p(G) for 1 ≦ p < ∞, p≠2, is a scalar multiple of an operator induced by a right translation.

Mathematical Subject Classification

Primary: 22.65

Milestones

Received: 8 August 1966

Published: 1 April 1968