Non-commutative LP-spaces
- 1 January 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 77 (1) , 91-102
- https://doi.org/10.1017/s0305004100049434
Abstract
1. Introduction. The spaces L1 and L2 of unbounded operators associated with a regular gauge space (von Neumann algebra equipped with a faithful normal semi-finite trace) are defined by Segal(5) definitions 3.3, 3.7. The spaces Lp (1 < p < ∞, p ± 2) are defined by Dixmier(2) as the abstract completions of their bounded parts. Dixmier makes use of the Riesz convexity theorem to prove the Hölder inequality, and the uniform convexity, and hence reflexivity, of LLp (2 < p < ∞).Keywords
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