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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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...
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)...
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.
Ky Fan (1987)
Mathematische Zeitschrift
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Peng Lizhong (1987)
Mathematica Scandinavica
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Lawrence G. Brown (1994)
Journal für die reine und angewandte Mathematik
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Giovanni Panti (2011)
Acta Arithmetica
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László Zsidó (2012)
Banach Center Publications
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The Tomita-Takesaki Theory is very complex and can be contemplated from different points of view. In the decade 1970-1980 several approaches to it appeared, each one seeking to attain more transparency. One of them was the paper of S. L. Woronowicz "Operator systems and their application to the Tomita-Takesaki theory" that appeared in 1979. Woronowicz's approach allows a particularly precise insight into the nature of the Tomita-Takesaki Theory and in this paper we present a brief, but...
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...
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.
T. V. Panchapagesan (1993)
Extracta Mathematicae
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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...
Santtu Ruotsalainen (2012)
Studia Mathematica
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Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators...
Gelu Popescu (1991)
Mathematica Scandinavica
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