Modification of the alternating direction implicit method and connections with von Neumann's method
H. Woźniakowski (1971)
Applicationes Mathematicae
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H. Woźniakowski (1971)
Applicationes Mathematicae
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Hichem Ben-El-Mechaiekh, Robert Dimand (2007)
Banach Center Publications
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Otto Moeschlin (2006)
Banach Center Publications
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Leszek Jan Ciach (1988)
Colloquium Mathematicae
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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...
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.
Ky Fan (1987)
Mathematische Zeitschrift
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Giovanni Panti (2011)
Acta Arithmetica
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Bikchentaev, A. M. (2004)
Lobachevskii Journal of Mathematics
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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)...
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...
Peng Lizhong (1987)
Mathematica Scandinavica
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T. V. Panchapagesan (1993)
Extracta Mathematicae
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Eva Hensz, Ryszard Jajte (1986)
Mathematische Zeitschrift
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Gelu Popescu (1991)
Mathematica Scandinavica
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Ravindran, K.T., Sudheer, K. (2010)
APPS. Applied Sciences
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Carlo Cecchini, Dénes Petz (1993)
Colloquium Mathematicae
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In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von...