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...