Semigroups of quasinormal operators

Mary Rodriguez Embry

Vol. 101 (1982), No. 1, 103–113

DOI: 10.2140/pjm.1982.101.103

Abstract

Strongly continuous semi-groups {Q_t} of quasinormal operators on Hilbert space are characterized as follows: there exist Hilbert spaces ℒ and 𝒦, a strongly continuous normal semi-group {N_t} on ℒ and a strongly continuous self-adjoint semi-group {h(t)} on 𝒦 such that {Q_t} is unitarily equivalent to {N_t}⊕ {h(t)L_t} on ℒ⊕ ℒ²(𝒦), where {L_t} is the forward translation semi-group on ℒ²(𝒦) and (h(t)f)(x) = h(t)f(x) a.e. for each f in ℒ²(𝒦).

Mathematical Subject Classification 2000

Primary: 47D05, 47D05

Secondary: 47B20

Milestones

Received: 1 May 1981

Published: 1 July 1982