Operator algebras generated by commuting projections: a vector measure approach

DOI10.1007/BFb0096184zbMath0936.47020MaRDI QIDQ1805573

Werner J. Ricker

Publication date: 11 November 1999

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

spectral measurerepresentation theoremsBoolean algebra of projectionsBade completenessBade reflexivity theoremRybakov's theorem on control measuresscalar type spectral operator

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Stone spaces (Boolean spaces) and related structures (06E15) Spectral operators, decomposable operators, well-bounded operators, etc. (47B40) Algebras of operators on Banach spaces and other topological linear spaces (47L10)

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Abelian von Neumann algebras, measure algebras and \(L^\infty\)-spaces ⋮ Bicommutants of multiplication operators ⋮ Strict topologies and spectral measures ⋮ Extension and integral representation of the finite Hilbert transform in rearrangement invariant spaces ⋮ TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY ⋮ Approximation of \(p\)-multiplier operators via their spectral projections ⋮ Operator algebras with contractive approximate identities: A large operator algebra in $c_0$ ⋮ Fourier multipliers and spectral measures in Banach function spaces ⋮ Boolean algebras of projections in (DF)-and (LF)-spaces ⋮ Weak completeness properties of the $L^1 $-space of a spectral measure ⋮ Integration with respect to Baire vector measures with applications to the spectral theory

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