Algebras of unbounded scalar-type spectral operators

P. G. Dodds, B. De Pagter

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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 ∫Ω fdP, 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 fdP if and only if T leaves invariant each closed subspace of X which is invariant under the range of the spectral measure P.

Original languageEnglish
Pages (from-to)41-74
Number of pages34
JournalPacific Journal of Mathematics
Volume130
Issue number1
DOIs
Publication statusPublished - Nov 1987

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