Some remarks on the convergence in measure and on a dominated sequence of operators measurable with respect to a semifinite von Neumann algebra
Leszek Jan Ciach (1988)
Colloquium Mathematicae
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Leszek Jan Ciach (1988)
Colloquium Mathematicae
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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. ...
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.
Hichem Ben-El-Mechaiekh, Robert Dimand (2007)
Banach Center Publications
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Otto Moeschlin (2006)
Banach Center Publications
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H. Woźniakowski (1971)
Applicationes Mathematicae
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Leszek J. Ciach
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CONTENTSIntroduction...............................................................................................................................................5§0. Fundamental definitions and notations...............................................................................................7§1. Subadditive measure on projectors of a von Neumann algebra.........................................................8§2. m-measurable operators. Convergence in measure.........................................................................10§3....
J. Chabrowski (2007)
Colloquium Mathematicae
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We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
Jan Chabrowski, Jianfu Yang (2005)
Annales Polonici Mathematici
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We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.
Michael Skeide (2006)
Banach Center Publications
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The category of von Neumann correspondences from 𝓑 to 𝓒 (or von Neumann 𝓑-𝓒-modules) is dual to the category of von Neumann correspondences from 𝓒' to 𝓑' via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the categories of representations of two von Neumann algebras) switches into Blecher's Eilenberg-Watts theorem...
Ky Fan (1987)
Mathematische Zeitschrift
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Jan Hamhalter (1992)
Mathematica Bohemica
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It is shown that every von Neumann algebra whose centre determines the state space is already abelian.
Robert Pluta, Bernard Russo (2015)
Studia Mathematica
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It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple)...
Giovanni Panti (2011)
Acta Arithmetica
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Stanisław Goldstein (1984)
Studia Mathematica
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Peng Lizhong (1987)
Mathematica Scandinavica
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Carlo Cecchini (1998)
Banach Center Publications
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The aim of this paper is to study markovianity for states on von Neumann algebras generated by the union of (not necessarily commutative) von Neumann subagebras which commute with each other. This study has been already begun in [2] using several a priori different notions of noncommutative markovianity. In this paper we assume to deal with the particular case of states which define odd stochastic couplings (as developed in [3]) for all couples of von Neumann algebras involved. In this...