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Małgorzata Pułka - One of the best experts on this subject based on the ideXlab platform.
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Prevalence problem in the set of quadratic stochastic operators acting on L1
arXiv: Probability, 2015Co-Authors: Krzysztof Bartoszek, Małgorzata PułkaAbstract:This paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 Space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
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Asymptotic properties of quadratic stochastic operators acting on the L1 Space
Nonlinear Analysis: Theory Methods & Applications, 2015Co-Authors: Krzysztof Bartoszek, Małgorzata PułkaAbstract:Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the L1 Space. It turns out that inprinciple most of the resu ...
Krzysztof Bartoszek - One of the best experts on this subject based on the ideXlab platform.
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Prevalence problem in the set of quadratic stochastic operators acting on L1
arXiv: Probability, 2015Co-Authors: Krzysztof Bartoszek, Małgorzata PułkaAbstract:This paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 Space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
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Asymptotic properties of quadratic stochastic operators acting on the L1 Space
Nonlinear Analysis: Theory Methods & Applications, 2015Co-Authors: Krzysztof Bartoszek, Małgorzata PułkaAbstract:Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the L1 Space. It turns out that inprinciple most of the resu ...
Novikov A. - One of the best experts on this subject based on the ideXlab platform.
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L1 -Space for a positive operator affiliated with von Neumann algebra
2020Co-Authors: Novikov A.Abstract:© 2016, Springer International Publishing.In this paper we suggest an approach for constructing an L1-type Space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we introduce a seminorm, and prove that it is a norm if and only if the operator is injective. For this norm we construct an L1-type Space as the complition of the Space of hermitian ultraweakly continuous linear functionals on von Neumann algebra, and represent L1-type Space as a Space of continuous linear functionals on the Space of special sesquilinear forms. Also, we prove that L1-type Space is isometrically isomorphic to the predual of von Neumann algebra in a natural way. We give a small list of alternate definitions of the seminorm, and a special definition for the case of semifinite von Neumann algebra, in particular. We study order properties of L1-type Space, and demonstrate the connection between semifinite normal weights and positive elements of this Space. At last, we construct a similar L-Space for the positive element of C*-algebra, and study the connection between this L-Space and the L1-type Space in case when this C*-algebra is a von Neumann algebra
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L1-Space for a positive operator affiliated with von Neumann algebra
2020Co-Authors: Novikov A.Abstract:© 2016 Springer International PublishingIn this paper we suggest an approach for constructing an (Formula presented.)-type Space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we introduce a seminorm, and prove that it is a norm if and only if the operator is injective. For this norm we construct an (Formula presented.)-type Space as the complition of the Space of hermitian ultraweakly continuous linear functionals on von Neumann algebra, and represent (Formula presented.)-type Space as a Space of continuous linear functionals on the Space of special sesquilinear forms. Also, we prove that (Formula presented.)-type Space is isometrically isomorphic to the predual of von Neumann algebra in a natural way. We give a small list of alternate definitions of the seminorm, and a special definition for the case of semifinite von Neumann algebra, in particular. We study order properties of (Formula presented.)-type Space, and demonstrate the connection between semifinite normal weights and positive elements of this Space. At last, we construct a similar L-Space for the positive element of C*-algebra, and study the connection between this L-Space and the (Formula presented.)-type Space in case when this C*-algebra is a von Neumann algebra
Erik J. Balder - One of the best experts on this subject based on the ideXlab platform.
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From Weak to Strong Convergence in L1-Spaces via K-Convergence (*).
Annali di Matematica Pura ed Applicata, 1993Co-Authors: Erik J. BalderAbstract:A generalized version of Komlos' theorem [6], combined with a useful property of denting points in the style of [17,22], gives a new, very efficient proof of Visintin's theorem and its generalizations [24,2,10,21,7], on equivalence of weak and strong convergence in L1-Space under denting point conditions.
Wu Hong-xing - One of the best experts on this subject based on the ideXlab platform.
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The Spectral Analysis of Transport Operator with Reflecting Boundary Condition in Slab Geometry
Mathematics in Practice and Theory, 2008Co-Authors: Wu Hong-xingAbstract:The objective of this paper is to research spectral analysis of transport operator with anisotropic continuous energy nonhomogeneous slab geometry in reflecting boundary condition.it proves the transport operator generates a C0 semigroup and the second-order remained term of the Dyson-Phillips expansion for the C0 semigroup is compact in Lp(1p∞) Space and weakly compact in L1 Space,and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite algebraic multiplicity in trip Γ,and to prove the existence of the dominand eigenvalue.
