Classification of nuclear C*-algebras. Entropy in operator algebras

Bibliographic Information

Classification of nuclear C*-algebras. Entropy in operator algebras

M. Rørdam, E. Størmer

(Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 126 . Operator algebras and non-commutative geometry / subseries editores, Joachim Cuntz, Vaughan F. R. Jones ; 7)

Springer, c2010

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Includes bibliographical references

Description and Table of Contents

Description

to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

Table of Contents

I. Classification of Nuclear, Simple C*-algebras.- II. A Survey of Noncommutative Dynamical Entropy.

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Details

  • NCID
    BB06487270
  • ISBN
    • 9783642076053
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin
  • Pages/Volumes
    vii, 198 p.
  • Size
    23 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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