The Kadec-Klee property in symmetric spaces of measurable operators

DOI10.1007/BF02774037zbMath0871.46034MaRDI QIDQ1355261

Pheodor A. Sukochev, Peter G. Dodds, Vladimir I. Chilin

Publication date: 30 September 1997

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Kadec-Klee propertysemifinite von Neumann algebra\(\tau\)-measurable operatorsseparable symmetric Banach function space on the positive half-line

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) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51)

Related Items (16)

\(\Phi\)-moment inequalities for independent and freely independent random variables ⋮ Banach-Saks property in Marcinkiewicz spaces ⋮ On Arazy's problem concerning isomorphic embeddings of ideals of compact operators ⋮ Isometries of symmetric operator spaces associated with AFD factors of type II and symmetric vector-valued spaces ⋮ The Grothendieck property in Marcinkiewicz spaces ⋮ Lifting of Kadec-Klee properties to symmetric spaces of measurable operators ⋮ Positive linear isometries in symmetric operator spaces ⋮ Normed Köthe spaces: a non-commutative viewpoint ⋮ Johnson-Schechtman inequalities in the free probability theory ⋮ A Lidskii type formula for Dixmier traces ⋮ Series of independent random variables in rearrangement invariant spaces: an operator approach ⋮ Sets of uniformly absolutely continuous norm in symmetric spaces of measurable operators ⋮ Catalysis in the trace class and weak trace class ideals ⋮ Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals ⋮ 2-co-lacunary sequences in noncommutative symmetric Banach spaces ⋮ \(k\)-extreme points in symmetric spaces of measurable operators

Cites Work

• Non-commutative Banach function spaces
• Notes on non-commutative integration
• Fully symmetric operator spaces
• Generalized s-numbers of \(\tau\)-measurable operators
• Noncommutative Kothe Duality
• Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$
• Convergence in Trace Ideals
• More on Convergence in Unitary Matrix Spaces
• A Lattice Renorming Theorem and Applications to Vector-Valued Processes
• Non-isomorphism of 𝐿_{𝑝}-spaces associated with finite and infinite von Neumann algebras
• Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions
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