Non-commutative Lorentz spaces associated with a semi-finite von Neumann algebra and applications

DOI10.3792/pjaa.57.303zbMath0491.46052OpenAlexW1964480920MaRDI QIDQ1167389

Hideki Kosaki

Publication date: 1981

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.57.303

zbMATH Keywords

intermediate spacesreal interpolationMarcinkiewicz interpolation theoremdominated convergence theoremsK-method of Peetrenon-commutative Lorentz spacesPowers-Stormer inequalitysemi-finite von Neumann algebra with a faithful semi-finite normal trace

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) General theory of von Neumann algebras (46L10) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Abstract interpolation of topological vector spaces (46M35)

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Majorizations for generalized s-numbers in semifinite von Neumann algebras, Ergodic theorems in fully symmetric spaces of τ-measurable operators, Fourier multipliers and group von Neumann algebras, Non-commutative Banach function spaces, Lipschitz continuity of the absolute value and Riesz projections in symmetric operator spaces, SOME ASPECTS OF THE THEORY OF SYMMETRIC OPERATOR SPACES, Rosenthal inequalities in noncommutative symmetric spaces, Sums of commutators in non-commutative Banach function spaces., Some results on non-commutative Banach function spaces, Convergence rates for weighted sums in noncommutative probability space, \(L^p-L^q\) multipliers on locally compact groups, Fully symmetric operator spaces, Introduction to the theory of noncommutative integration, Interpolation theory and the Wigner-Yanase-Dyson-Lieb concavity

Cites Work

• Duality for crossed products and the structure of von Neumann algebras of type III
• Notes on non-commutative integration
• A non-commutative extension of abstract integration
• L p Fourier Transforms on Locally Compact Unimodular Groups
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