Pointwise Convergence Theorems in L2 over a von Neumann Algebra.

Eva Hensz; Ryszard Jajte

Displaying similar documents to “Pointwise Convergence Theorems in L2 over a von Neumann Algebra.”

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Bundle Convergence in a von Neumann Algebra and in a von Neumann Subalgebra

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Let H be a separable complex Hilbert space, 𝓐 a von Neumann algebra in 𝓛(H), ϕ a faithful, normal state on 𝓐, and 𝓑 a commutative von Neumann subalgebra of 𝓐. Given a sequence (Xₙ: n ≥ 1) of operators in 𝓑, we examine the relations between bundle convergence in 𝓑 and bundle convergence in 𝓐.

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Banach principle in the space of τ-measurable operators

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We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.