Compact operators, invariant subspaces, and spectral synthesis

DOI10.1016/0022-1236(88)90110-3zbMath0681.47019OpenAlexW1973624300MaRDI QIDQ1823442

John Froelich

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0022-1236(88)90110-3

zbMATH Keywords

invariant subspacescommutative subspace latticeCSL-algebraset of spectral synthesiscompact pseudo-integral operatorsmultiplicity in the sense of harmonic analysisoperators of Schatten p-class

Mathematics Subject Classification ID

Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Abstract operator algebras on Hilbert spaces (47L30) Invariant subspaces of linear operators (47A15) Spectral synthesis on groups, semigroups, etc. (43A45)

Related Items (24)

On the connection between sets of operator synthesis and sets of spectral synthesis for locally compact groups ⋮ Operator synthesis. I: Synthetic sets, bilattices and tensor algebras ⋮ Reduced spectral synthesis and compact operator synthesis ⋮ Closable multipliers ⋮ Synthetic properties of locally compact groups: preservation and transference ⋮ Fourier algebras on homogeneous spaces ⋮ Ranges of bimodule projections and reflexivity ⋮ Completely distributive CSL algebras with no complements in $\mathcal {C}_p$ ⋮ Malliavin's theorem for weak synthesis on nonabelian groups ⋮ Problems about reflexive algebras ⋮ On perturbations of reflexive algebras ⋮ Invariant subspaces and thin sets ⋮ A Note on Compact Ideal Perturbations in Semifinite von Neumann Algebras ⋮ Spectral synthesis in the Fourier algebra and the Varopoulos algebra ⋮ Compact Perturbations of Certain CSL Algebras ⋮ Regularity for Operator Algebras on a Hilbert Space ⋮ Sets of p-multiplicity in locally compact groups ⋮ Operator synthesis and tensor products ⋮ Ideals of \(A(G)\) and bimodules over maximal abelian selfadjoint algebras ⋮ Rank one subspaces of bimodules over maximal abelian selfadjoint algebras ⋮ REFLEXIVITY OF THE TRANSLATION-DILATION ALGEBRAS ON L²(ℝ) ⋮ Compact operators, invariant subspaces, and spectral synthesis ⋮ On synthetic and transference properties of group homomorphisms ⋮ Sets of multiplicity and closable multipliers on group algebras

Cites Work

• Perturbation theory for groups and lattices
• The carrier space of a reflexive operator algebra
• Continuous singular measures with small Fourier-Stieltjes transforms
• The radical of a reflexive operator algebra
• Operator algebras and invariant subspaces
• An operator algebra which is not closed in the Calkin algebra
• Compact operators, invariant subspaces, and spectral synthesis
• Tensor Products of Reflexive Algebras
• Tensor Products of Reflexive Algebras II
• The Slice Map Problem for σ-Weakly Closed Subspaces of Von Neumann Algebras
• Similarity and compact perturbations of nest algebras.
• A Note on Rank-One Operators in Reflexive Algebras
• Pseudo-Integral Operators
• Ten problems in Hilbert space
• Support preserving measure algebras and spectral synthesis
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