Completeness of symmetric Δ-normed spaces of τ-measurable operators

Jinghao Huang; Galina Levitina; Fedor Sukochev

doi:10.4064/sm8349-10-2016

Completeness of symmetric Δ-normed spaces of τ-measurable operators

Jinghao Huang, Galina Levitina, Fedor Sukochev

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Let M be an arbitrary semifinite von Neumann algebra equipped with a faithful normal semifinite trace and φ let E be a complete symmetric Δ-normed function space. We show that the corresponding symmetric space E(M; φ ) of -measurable operators in S(M; φ) is a complete symmetrically δ-normed ideal.

Original language	English
Pages (from-to)	201-219
Number of pages	19
Journal	Studia Mathematica
Volume	237
Issue number	3
DOIs	https://doi.org/10.4064/sm8349-10-2016
Publication status	Published - 2017
Externally published	Yes

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title = "Completeness of symmetric Δ-normed spaces of τ-measurable operators",

abstract = "Let M be an arbitrary semifinite von Neumann algebra equipped with a faithful normal semifinite trace and φ let E be a complete symmetric Δ-normed function space. We show that the corresponding symmetric space E(M; φ ) of -measurable operators in S(M; φ) is a complete symmetrically δ-normed ideal.",

keywords = "Calkin correspondence, Symmetric Δ-ideals, τ-measurable operators.",

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AU - Huang, Jinghao

AU - Levitina, Galina

AU - Sukochev, Fedor

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PY - 2017

Y1 - 2017

N2 - Let M be an arbitrary semifinite von Neumann algebra equipped with a faithful normal semifinite trace and φ let E be a complete symmetric Δ-normed function space. We show that the corresponding symmetric space E(M; φ ) of -measurable operators in S(M; φ) is a complete symmetrically δ-normed ideal.

AB - Let M be an arbitrary semifinite von Neumann algebra equipped with a faithful normal semifinite trace and φ let E be a complete symmetric Δ-normed function space. We show that the corresponding symmetric space E(M; φ ) of -measurable operators in S(M; φ) is a complete symmetrically δ-normed ideal.

KW - Calkin correspondence

KW - Symmetric Δ-ideals

KW - τ-measurable operators.

UR - https://www.scopus.com/pages/publications/85018526015

U2 - 10.4064/sm8349-10-2016

DO - 10.4064/sm8349-10-2016

M3 - Article

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VL - 237

SP - 201

EP - 219

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

Completeness of symmetric Δ-normed spaces of τ-measurable operators

Abstract

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