Mathematical theory of von Neumann economic models. Report on recent results
Jerzy Łoś (1979)
Colloquium Mathematicae
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Jerzy Łoś (1979)
Colloquium Mathematicae
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Marchi, Ezio, Tarazaga, Pablo, Elorza, Enrique (1983-1984)
Portugaliae mathematica
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Otto Moeschlin (2006)
Banach Center Publications
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Hichem Ben-El-Mechaiekh, Robert Dimand (2007)
Banach Center Publications
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H. Woźniakowski (1971)
Applicationes 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...
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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Milan Mareš (1986)
Kybernetika
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Giovanni Panti (2011)
Acta Arithmetica
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H. Abele (1977)
Metrika
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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)...
Peng Lizhong (1987)
Mathematica Scandinavica
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François Castella (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann...
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.