Noncommutative Calderón-Lozanovskiĭ-Hardy spaces
type: Item
instance of: scholarly article
title: Noncommutative Calderón-Lozanovskiĭ-Hardy spaces
zbMATH Open document ID: 1468.46069
author: Jingjing Shao
author: Cheng Yan
author: Yazhou Han
published in: Positivity
publication date: 2021-05-07T00:00:00Z
review text: Let \(\mathcal M\) be a von Neumann algebra with a faithful normal semi-finite trace \(\tau\) and let $E$ be a symmetric quasi-Banach space. For any Orlicz function \(\varphi\), we can define the noncommutative Calderón-Lozanovskiĭ spaces \(E_{\varphi}(\mathcal M)\). In the present paper, the authors give several properties of those spaces similar to those of their classical counterparts. Specifically, by introducing a noncommutative Calderón-Lozanovskiĭ space \(E_{\varphi}(\mathcal M)\), the authors give the multiplication operator space and the complex interpolation on \(E_{\varphi}(\mathcal M)\). Furthermore, based on a semi-finite subdiagonal algebra \(\mathcal A\) with respect to a faithful normal expectation \(\mathcal E\) such that \(\tau\circ\mathcal E=\tau\) in \(\mathcal M\), the authors introduce a noncommutative Calderón-Lozanovskiĭ-Hardy space \(H^{\varphi}(\mathcal A)\) and transfer the recent results of the noncommutative Hardy space to this version. For example, certain complex interpolation theorems as well as factorization theorems are obtained. At last, a new version of Beurling's theorem for \(\mathcal A\)-invariant subspaces in noncommutative Calderón-Lozanovskiĭ-Hardy spaces is proved.
Mathematics Subject Classification ID: 46L52
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46L53
zbMATH DE Number: 7345586
zbMATH Keywords: von Neumann algebras
zbMATH Keywords: subdiagonal subalgebras
zbMATH Keywords: noncommutative Hardy spaces
zbMATH Keywords: multiplication operator spaces
zbMATH Keywords: complex interpolation spaces
zbMATH Keywords: noncommutative Calderón-Lozanovskiĭ spaces
reviewed by: Guoxing Ji
MaRDI profile type: Publication
full work available at URL: s11117-020-00779-1
OpenAlex ID: W3041779985
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DOI: 10.1007/S11117-020-00779-1
description: scientific article; zbMATH DE number 7345586