One parameter groups of isometries on certain Banach spaces

Richard Joseph Fleming, Jerome A. Goldstein and James E. Jamison

Vol. 64 (1976), No. 1, 145–151

DOI: 10.2140/pjm.1976.64.145

Abstract

Banach spaces of class 𝒮 were introduced by Fleming and Jamison. This broad class includes all Banach spaces having hyperorthogonal Schauder bases and, in particular, 𝒮 includes all Orlicz spaces L^Φ on an atomic measure space such that the characteristic functions of the atoms form a basis for L^Φ. The main theorem gives the structure of one parameter strongly continuous (or (C₀)) groups of isometries on Banach spaces of class 𝒮. Other results correct and complement the work of Goldstein on groups of isometries on Orlicz spaces over atomic measure spaces.

Mathematical Subject Classification 2000

Primary: 46B99

Secondary: 47D10

Milestones

Received: 26 June 1974

Published: 1 May 1976