Vol. 130, No. 1, 1987

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Algebras of unbounded scalar-type spectral operators

Peter Gerard Dodds and Bernardus de Pagter

Vol. 130 (1987), No. 1, 41–74
Abstract

If P : Σ →ℒ(X) is a closed spectral measure in the quasicomplete locally convex space X and if T is a densely defined linear operator in X with domain invariant under each operator of the form Ωf dP, with f a complex bounded Σ-measurable function then T is closable and there exists a complex Σ-measurable function f such that the closure of T is the spectral integral Ω f dP if and only if T leaves invariant each closed subspace of X which is invariant under the range of the spectral measure P.

Mathematical Subject Classification 2000
Primary: 47D40, 47D40
Secondary: 47B40
Milestones
Received: 17 April 1986
Published: 1 November 1987
Authors
Peter Gerard Dodds
Bernardus de Pagter