Dominated convergence theorems in Haagerup noncommutative Lp -spaces


Bekjan T.N. Mustafa M.
April 2023Birkhauser

Advances in Operator Theory
2023#8Issue 2

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.

Almost uniform convergence , Dominated convergence , Haagerup noncommutative Lp-spaces

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Astana IT University, Astana, 010000, Kazakhstan
Department of Mathematics, SSH, Nazarbayev University, 53 Kabanbay Batyr Avenue, Astana, 010000, Kazakhstan

Astana IT University
Department of Mathematics

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