Dominated convergence theorems in Haagerup noncommutative Lp -spaces

Turdebek N. Bekjan; Manat Mustafa

doi:10.1007/s43036-023-00261-1

Dominated convergence theorems in Haagerup noncommutative L_p -spaces

Turdebek N. Bekjan, Manat Mustafa

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

Abstract

Let M be a σ-finite von Neumann algebra and T: M→ M be a linear bounded positive map under some natural conditions. We obtain that if (xn)n≥1 is a sequence in M converging to x almost uniformly and (xn)n≥1 satisfies certain domination condition, then (T(xn))n≥1 converges to T(x) almost uniformly.

Original language	English
Article number	34
Journal	Advances in Operator Theory
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s43036-023-00261-1
Publication status	Published - Apr 2023

Keywords

Almost uniform convergence
Dominated convergence
Haagerup noncommutative L-spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

Access to Document

10.1007/s43036-023-00261-1

Cite this

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title = "Dominated convergence theorems in Haagerup noncommutative Lp -spaces",

abstract = "Let M be a σ-finite von Neumann algebra and T: M→ M be a linear bounded positive map under some natural conditions. We obtain that if (xn)n≥1 is a sequence in M converging to x almost uniformly and (xn)n≥1 satisfies certain domination condition, then (T(xn))n≥1 converges to T(x) almost uniformly.",

keywords = "Almost uniform convergence, Dominated convergence, Haagerup noncommutative L-spaces",

author = "Bekjan, {Turdebek N.} and Manat Mustafa",

note = "Funding Information: We thank the reviewer for useful comments. The work was supported by Nazarbayev University Faculty Development Competitive Research Grants 021220FD3851. T. B. Bekjan is partially supported by the Science Committee of the Ministry of Science and High Education of the Republic of Kazakhstan (Grant no. AP14870431). Publisher Copyright: {\textcopyright} 2023, Tusi Mathematical Research Group (TMRG).",

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T1 - Dominated convergence theorems in Haagerup noncommutative Lp -spaces

AU - Bekjan, Turdebek N.

AU - Mustafa, Manat

N1 - Funding Information: We thank the reviewer for useful comments. The work was supported by Nazarbayev University Faculty Development Competitive Research Grants 021220FD3851. T. B. Bekjan is partially supported by the Science Committee of the Ministry of Science and High Education of the Republic of Kazakhstan (Grant no. AP14870431). Publisher Copyright: © 2023, Tusi Mathematical Research Group (TMRG).

PY - 2023/4

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N2 - Let M be a σ-finite von Neumann algebra and T: M→ M be a linear bounded positive map under some natural conditions. We obtain that if (xn)n≥1 is a sequence in M converging to x almost uniformly and (xn)n≥1 satisfies certain domination condition, then (T(xn))n≥1 converges to T(x) almost uniformly.

AB - Let M be a σ-finite von Neumann algebra and T: M→ M be a linear bounded positive map under some natural conditions. We obtain that if (xn)n≥1 is a sequence in M converging to x almost uniformly and (xn)n≥1 satisfies certain domination condition, then (T(xn))n≥1 converges to T(x) almost uniformly.

KW - Almost uniform convergence

KW - Dominated convergence

KW - Haagerup noncommutative L-spaces

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