TY - JOUR

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

Y1 - 2023/4

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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U2 - 10.1007/s43036-023-00261-1

DO - 10.1007/s43036-023-00261-1

M3 - Article

AN - SCOPUS:85153049582

SN - 2538-225X

VL - 8

JO - Advances in Operator Theory

JF - Advances in Operator Theory

IS - 2

M1 - 34

ER -