The existence of spectral decompositions in \(L^ p\)-subspaces

DOI10.3792/PJAA.61.172zbMath0575.42011OpenAlexW1968463327MaRDI QIDQ1064491

Earl Berkson, T. Alastair Gillespie

Publication date: 1985

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.61.172

zbMATH Keywords

Banach spacesFourier-Stieltjes transformprojection-valued functionoperator-valued Fourier series

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Functional calculus for linear operators (47A60) Multipliers in one variable harmonic analysis (42A45) Spectral operators, decomposable operators, well-bounded operators, etc. (47B40)

Cites Work

• Spectral families of projections in Hardy spaces
• Stečkin's theorem, transference, and spectral decompositions
• Logarithms in multiplier algebras
• A Spectral Theorem for L^p Translations
• Spectral Families of Projections, Semigroups, and Differential Operators
• Spectral decomposition of ergodic flows on 𝐿^{𝑝}
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