The structure of a special class of weighted translation semigroups

Mary Rodriguez Embry and Alan Leslie Lambert

Vol. 75 (1978), No. 2, 359–371

DOI: 10.2140/pjm.1978.75.359

Abstract

A special class of weighted translation semigroups {S_t} on ℒ²(ℛ₊) is studied. The weakly closed algebra 𝒜 generated by the semigroup is maximal abelian and the spectra of elements of 𝒜 are studied. It is shown that each densely defined linear transformation commuting with 𝒜 is closable and that every transitive algebra containing 𝒜 is weakly dense in the full algebra of operators on L²(ℛ₊).

Mathematical Subject Classification

Primary: 47D05, 47D05

Milestones

Received: 20 April 1977

Revised: 2 June 1977

Published: 1 April 1978