Displaying similar documents to “Subadditive measures on projectors of a von Neumann algebra”

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

Barthélemy Le Gac, Ferenc Móricz (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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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.

Noncommutative Poincaré recurrence theorem

Andrzej Łuczak (2001)

Colloquium Mathematicae

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Poincaré’s classical recurrence theorem is generalised to the noncommutative setup where a measure space with a measure-preserving transformation is replaced by a von Neumann algebra with a weight and a Jordan morphism leaving the weight invariant. This is done by a suitable reformulation of the theorem in the language of L ∞ -space rather than the original measure space, thus allowing the replacement of the commutative von Neumann algebra L ∞ by a noncommutative one.

Dual algebras generated by von Neumann n-tuples over strictly pseudoconvex sets

Michael Didas

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Let D ⋐ X denote a relatively compact strictly pseudoconvex open subset of a Stein submanifold X ⊂ ℂⁿ and let H be a separable complex Hilbert space. By a von Neumann n-tuple of class over D we mean a commuting n-tuple of operators T ∈ L(H)ⁿ possessing an isometric and weak* continuous H ∞ ( D ) -functional calculus as well as a ∂D-unitary dilation. The aim of this paper is to present an introduction to the structure theory of von Neumann n-tuples of class over D including the necessary function-...

Smooth operators in the commutant of a contraction

Pascale Vitse (2003)

Studia Mathematica

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For a completely non-unitary contraction T, some necessary (and, in certain cases, sufficient) conditions are found for the range of the H ∞ calculus, H ∞ ( T ) , and the commutant, T’, to contain non-zero compact operators, and for the finite rank operators of T’ to be dense in the set of compact operators of T’. A sufficient condition is given for T’ to contain non-zero operators from the Schatten-von Neumann classes S p .

Sets of p-multiplicity in locally compact groups

I. G. Todorov, L. Turowska (2015)

Studia Mathematica

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We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E * = ( s , t ) : t s - 1 ∈ E is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.

Topologies on central extensions of von Neumann algebras

Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2012)

Open Mathematics

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Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra. ...