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Abelian Subalgebras of Von Neumann Algebras (American Mathematical Society.) by Donald Bures

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Published by American Mathematical Society .
Written in English

Subjects:

  • Algebra - General,
  • Mathematics

Book details:

The Physical Object
FormatPaperback
Number of Pages127
ID Numbers
Open LibraryOL11419848M
ISBN 100821818104
ISBN 109780821818107

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Genre/Form: Electronic books: Additional Physical Format: Print version: Bures, Donald. Abelian subalgebras of von Neumann algebras. Providence, R.I.: American.   The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann by: Title (HTML): Abelian Subalgebras of Von Neumann Algebras Author(s) (Product display): D. Bures Book Series Name: Memoirs of the American Mathematical Society. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras.

subalgebra for von Neumann algebras. These subalgebras, which we term complete, are proper generalizations of regular abelian subalgebras (i.e. those whose normal-izers in the ambient von Neumann algebra generate the ambient algebra), and yet are, in many respects, as well behaved and determining as regular abelian subalge-bras are. of these group measure space von Neumann algebras is in general a very hard problem. Nevertheless a lot of progress has been made on several fronts. One recurring theme in all known classification results is the special role played by the so-called Cartan subalgebras - maximal abelian subalgebras whose normalizer generates the II1 factor. Given. In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity is a special type of C*-algebra.. Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum .   In a semifinite von Neumann algebra we get the following charac- terization of smooth maximal abelian subalgebras which is just an application of Stermer's recent result [8, Theorem 2.b]. PROPOSITION Let M be a semifinite von Neumann algebra, then a maximal abelian subalgebra is smooth if and only if it is generated by finite projections.

Additional Physical Format: Online version: Bures, Donald. Abelian subalgebras of von Neumann algebras. Providence, R.I., American Mathematical Society,   - Buy Abelian Subalgebras of Von Neumann Algebras (Memoirs of the American Mathematical Society) book online at best prices in India on Read Abelian Subalgebras of Von Neumann Algebras (Memoirs of the American Mathematical Society) book reviews & author details and more at Free delivery on qualified : Paperback. states that hyperfinite von Neumann algebras are exactly the amenable ones. This characterization implies inparticularthatallvonNeumann subalgebras ofahyperfinite tracial von Neumann algebra are completely described: they are hyperfinite. Up to now, such an understanding of subalgebras is out of reach for a non-hyperfinite von Neumann algebra. subalgebra of the group von Neumann algebra is maximal abelian and singular. Moreover the Puk anszky invariant contains a type I 1summand. Introduction Let be a group acting simply transitively on the vertices of a ho-mogeneous tree T of degree n+ 1.