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Compact Derivations on Von Neumann Algebras
Canadian Mathematical Bulletin, 1981AbstractIf is a von Neumann algebra that thas no nonzero finite discrete central projection, then there is no nontrivial compact derivation of into itself.
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Injective von Neumann Algebras
2003We have finally come to the first highlight of the entire book. Both sections are devoted to the proof of the equivalence of the injectivity and the approximately finite dimensionality of a von Neumann algebra, Corollary 1.8 and Theorem 1.9. The implication: the AFD ⇒ the injectivity for a von Neumann algebra is an easy consequence of averaging over ...
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2011
This thesis carries out some of classical integration theory in the context of an operator algebra. The starting point is measure on the projections of an abelian von Neumann algebra. This yields an integral on the self-adjoint operators whose spectral projections lie in the algebra.
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This thesis carries out some of classical integration theory in the context of an operator algebra. The starting point is measure on the projections of an abelian von Neumann algebra. This yields an integral on the self-adjoint operators whose spectral projections lie in the algebra.
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Abstract This chapter serves to prepare the reader for the future interpretation of non-abelian von Neumann algebras as noncommutative L∞-spaces. We achieve this by presenting a proof of Maharam’s theorem interpreted from a von Neumann algebra perspective, which is in essence a structural classification of abelian von Neumann algebras ...
Stanisław Goldstein, Louis Labuschagne
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Stanisław Goldstein, Louis Labuschagne
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Von Neumann Algebras. C*-Algebras. W*-Algebras
1992The purpose of this section is to provide a brief glossary of mathematical terms, concepts and theorems which will be subsequently used. Proofs are only sketched or omitted altogether and the reader is referred to the bibliography at the end of the section to supplement this minimal exposition.
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Normalcy in Von Neumann Algebras
Proceedings of the London Mathematical Society, 1973openaire +1 more source