Vol. 64, No. 1, 1976

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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
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 LΦ on an atomic measure space such that the characteristic functions of the atoms form a basis for LΦ. 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
Authors
Richard Joseph Fleming
Jerome A. Goldstein
James E. Jamison