Operator Algebra and Dynamics, 1st Edition

  • Published By:
  • ISBN-10: 3642394590
  • ISBN-13: 9783642394591
  • DDC: 512.55
  • Grade Level Range: College Freshman - College Senior
  • 332 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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Based on presentations given at the NordForsk Network Closing Conference "Operator Algebra and Dynamics," held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a  broad spectrum of researchers and  students in mathematics, physics, and engineering.

Table of Contents

Front Cover.
Other Frontmatter.
Other Frontmatter.
Title Page.
Copyright Page.
List of Contributors.
1: The Haagerup Property for Discrete Measured Groupoids.
2: Do Phantom Cuntz-Krieger Algebras Exist?.
3: Projective Dimension in Filtrated K-Theory.
4: An Introduction to the C*-Algebra of a One-Sided Shift Space.
5: Classification of Graph C*-Algebras with No More than Four Primitive Ideals.
6: Remarks on the Pimsner-Voiculescu Embedding.
7: Graph C*-Algebras with a T1 Primitive Ideal Space.
8: The Law of Large Numbers for the Free Multiplicative Convolution.
9: Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?.
10: On the Grothendieck Theorem for Jointly Completely Bounded Bilinear Forms.
11: C*-Algebras Associated with a-adic Numbers.
12: The Structure of Stacey Crossed Products by Endomorphisms.
13: Quasi-symmetric Group Algebras and C*-Completions of Hecke Algebras.
14: Dynamics, Wavelets, Commutants and Transfer Operators Satisfying Crossed Product Type Commutation Relations.
15: On a Counterexample to a Conjecture by Blackadar.
16: The Topological Dimension of Type I C*-Algebras.