Cyclic multiplication operators on L_p-spaces

H. A. Seid

Vol. 51 (1974), No. 2, 549–562

DOI: 10.2140/pjm.1974.51.549

Abstract

Let (X,Σ,μ) be a measure space. Suppose f is in L_∞(X,Σ,μ). The operator M_f on L_p(X,Σ,μ) defined by M_f(g) = f ⋅g, for g in L_p(X,Σ,μ) is called a multiplication operator. The purpose of this paper is to characterize cyclic multiplication operators and to relate their structure to the properties of the measure space on which the underlying L_p-space is defined.

Mathematical Subject Classification 2000

Primary: 47B37

Milestones

Received: 6 December 1972

Published: 1 April 1974