Modular Theory in Operator Algebras
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The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by S.V. Stratila and L. Zsido) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.read more
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Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
TL;DR: In this article, the authors present a model for operators on Hilbert Space, including C*-Algebras, Von Neumann Algebra, and K-Theory and Finiteness.
Journal ArticleDOI
Locally compact quantum groups
Johan Kustermans,Stefaan Vaes +1 more
TL;DR: The theory of locally compact quantum groups that are studied in the framework of operator algebras, i.e., C*-alges and von Neumann alges, is introduced in this paper.
Journal ArticleDOI
Locally compact quantum groups in the von Neumann algebraic setting
Johan Kustermans,Stefaan Vaes +1 more
TL;DR: In this paper, the authors give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a $C^*$-algebraic quantum group.
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Noncommutative Burkholder/Rosenthal inequalities
Marius Junge,Quanhua Xu +1 more
TL;DR: The martingale inequalities in noncommutative Lp-spaces associated with a von Neumann algebra equipped with a faithful normal state were investigated in this paper, where they were shown to be equivalent to the non-commutativity of the classical Burkholder inequality on the conditioned (or little) square function.