Groups of isometries on Orlicz spaces

Jerome A. Goldstein

Vol. 48 (1973), No. 2, 387–393

DOI: 10.2140/pjm.1973.48.387

Abstract

If X is an Orlicz space of functions on an atomic measure space, then, roughly, the only strongly continuous groups of isometries on X are trivial, unless X is a Hilbert space. Hilbert space is thus characterized among the Orlicz spaces on an atomic measure space by its great abundance of strongly continuous isometric groups.

Mathematical Subject Classification 2000

Primary: 46E30

Milestones

Received: 14 December 1971

Revised: 6 January 1972

Published: 1 October 1973