The Haar System in the Preduals of Hyperfinite Factors

DOI10.4153/CMB-2011-007-7zbMATH Open1248.46042arXiv0808.2851OpenAlexW2963380682MaRDI QIDQ2882482

Denis Potapov, Fedor A. Sukochev

Publication date: 4 May 2012

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Abstract: We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types $hbox{II}_1$, $hbox{II}_{i}nfty$, $hbox{III}_{l}ambda$, $0<lambdaleq1$. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators (respectively, in any non-commutative $L^p$-space).

Full work available at URL: https://arxiv.org/abs/0808.2851

zbMATH Keywords

Schauder basesnoncommutative \(L^p\)-spacepreduals to the hyperfinite factors

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Noncommutative function spaces (46L52)

Related Items (2)

A remarkable rearrangement of the Haar system in $L_p$ ⋮ The Walsh basis in the \(L^p\)-spaces of hyperfinite \(\mathrm{III}_\lambda\) factors, \(0<\lambda\leq 1\)

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