Stečkin's theorem, transference, and spectral decompositions

DOI10.1016/0022-1236(87)90128-5zbMath0607.47027OpenAlexW2001237046MaRDI QIDQ1085416

Earl Berkson, T. Alastair Gillespie

Publication date: 1987

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(87)90128-5

zbMATH Keywords

diagonalizationpower-bounded operatorsstrong operator topologyFourier-Stieltjes transform of a projection- valued mappingStečkin's theoremtype (B)uniformly bounded one-parameter groupwell bounded

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Spectral operators, decomposable operators, well-bounded operators, etc. (47B40)

Related Items

\(A_{p}\) weights and strong convergence of operator-valued Fourier series for Stieltjes convolutions of Marcinkiewicz functions, Logarithms of isometries and their spectral decompositions in Hardy spaces, Fourier series criteria for operator decomposability, A transference principle for general groups and functional calculus on UMD spaces, The \(q\)-variation of functions and spectral integration of Fourier multipliers, Spectral Decompositions of One-Parameter Groups of Isometries on Hardy Spaces, Operational calculus and integral transforms for groups with finite propagation speed, Examples of unbounded imaginary powers of operators, On the almost everywhere convergence of ergodic averages for power- bounded operators on \(L^ p\) subspaces, Fourier multipliers in Banach function spaces with UMD concavifications, Operator ergodic theory for one-parameter decomposable groups, Hilbert, Dirichlet and Fejér families of operators arising from \(C_0\)-groups, cosine functions and holomorphic semigroups, Vector valued \(q\)-variation for ergodic averages and analytic semigroups, Mean-boundedness and Littlewood-Paley for separation-preserving operators, The Banach algebras \(AC(\sigma)\) and \(BV(\sigma)\), The existence of spectral decompositions in \(L^ p\)-subspaces

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