On symmetric embedding of type I factors
29 Jan 2021-Journal of Mathematical Physics (AIP Publishing LLCAIP Publishing)-Vol. 62, Iss: 1, pp 013511
TL;DR: In this article, Buchholz, D'Antoni, and Longo proved that the symmetric embedding of B(H) into any of its bimodules induced by Markov maps is compact.
Abstract: In this paper, we provide a direct proof of the fact that the symmetric embedding of B(H) into any of its bimodules induced by Markov maps is compact and establishes that this property characterizes type I factors. This is an extension of a result of D. Buchholz, C. D’Antoni, and R. Longo [J. Funct. Anal. 88(2), 233–250 (1990)].
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TL;DR: In this paper , it was shown that the factorization of the Araki-Woods von Neumann algebras is equivalent to the factorisation of all the factors for all the q-deformed arameans.
Abstract: The $q$-deformed Araki-Woods von Neumann algebras $\Gamma_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ are factors for all $q\in (-1,1)$ whenever $dim(\mathcal{H}_\mathbb{R})\geq 3$. When $dim(\mathcal{H}_\mathbb{R})=2$ they are factors as well for all $q$ so long as the parameter defining $(U_t)$ is `small' or $1$ $($trivial$)$ as the case may be.
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Book•
01 Jan 2001
TL;DR: In this article, the basic concepts in Banach spaces are discussed, including weak topologies, uniform convexity, smoothness and structure, and weakly compactly generated spaces.
Abstract: Preface * 1 Basic Concepts in Banach Spaces * 2 Hahn-Banach and Banach Open Mapping Theorems * 3 Weak Topologies * 4 Locally Convex Spaces * 5 Structure of Banach Spaces * 6 Schauder Bases * 7 Compact Operators on Banach Spaces * 8 Differentiability of Norms * 9 Uniform Convexity * 10 Smoothness and Structure * 11 Weakly Compactly Generated Spaces * 12 Topics in Weak Toplogy * References * Index
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