Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces

Zhenhua Ma; Lining Jiang; Kai Ji

doi:10.1016/j.jmaa.2017.09.043

Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces

Zhenhua Ma, Lining Jiang^*, Kai Ji

^*Corresponding author for this work

School of Mathematics and Statistics

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

Abstract

This paper studies the Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces L_φ(M˜,τ), where M˜ is the space of τ-measurable operators, and φ is an Orlicz function. We show that L_φ(M˜,τ) has the Kadec–Klee property in measure if and only if the φ satisfies the Δ₂(∞) condition. As a corollary, the dual space and reflexivity of L_φ(M˜,τ) are given.

Original language	English
Pages (from-to)	1193-1202
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	458
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2017.09.043
Publication status	Published - 15 Feb 2018

Keywords

Kadec–Klee property
Noncommutative Orlicz spaces
Orlicz function
von Neumann algebra
τ-Measurable operator

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10.1016/j.jmaa.2017.09.043

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title = "Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces",

abstract = "This paper studies the Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces Lφ(M˜,τ), where M˜ is the space of τ-measurable operators, and φ is an Orlicz function. We show that Lφ(M˜,τ) has the Kadec–Klee property in measure if and only if the φ satisfies the Δ2(∞) condition. As a corollary, the dual space and reflexivity of Lφ(M˜,τ) are given.",

keywords = "Kadec–Klee property, Noncommutative Orlicz spaces, Orlicz function, von Neumann algebra, τ-Measurable operator",

author = "Zhenhua Ma and Lining Jiang and Kai Ji",

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AU - Ma, Zhenhua

AU - Jiang, Lining

AU - Ji, Kai

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N2 - This paper studies the Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces Lφ(M˜,τ), where M˜ is the space of τ-measurable operators, and φ is an Orlicz function. We show that Lφ(M˜,τ) has the Kadec–Klee property in measure if and only if the φ satisfies the Δ2(∞) condition. As a corollary, the dual space and reflexivity of Lφ(M˜,τ) are given.

AB - This paper studies the Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces Lφ(M˜,τ), where M˜ is the space of τ-measurable operators, and φ is an Orlicz function. We show that Lφ(M˜,τ) has the Kadec–Klee property in measure if and only if the φ satisfies the Δ2(∞) condition. As a corollary, the dual space and reflexivity of Lφ(M˜,τ) are given.

KW - Kadec–Klee property

KW - Noncommutative Orlicz spaces

KW - Orlicz function

KW - von Neumann algebra

KW - τ-Measurable operator

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SP - 1193

EP - 1202

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces

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Keywords

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