# Operator Theory, Operator Algebras, and Applications

Share this page *Edited by *
*Deguang Han; Palle E.T. Jorgensen; David Royal Larson*

This book offers a presentation of some new
trends in operator theory and operator algebras, with a view to their
applications. It consists of separate papers written by some of the
leading practitioners in the field. The content is put together by the
three editors in a way that should help students and working
mathematicians in other parts of the mathematical sciences gain
insight into an important part of modern mathematics and its
applications.

While different specialist authors are outlining new results in
this book, the presentations have been made user friendly with the aid
of tutorial material. In fact, each paper contains three things: a
friendly introduction with motivation, tutorial material, and new
research. The authors have strived to make their results relevant to
the rest of mathematics. A list of topics discussed in the book
includes wavelets, frames and their applications, quantum dynamics,
multivariable operator theory, \(C^*\)-algebras, and von Neumann
algebras. Some longer papers present recent advances on particular,
long-standing problems such as extensions and dilations, the
Kadison-Singer conjecture, and diagonals of self-adjoint
operators.

#### Readership

Graduate students and research mathematicians interested in theory of operators and operator algebras.

# Table of Contents

## Operator Theory, Operator Algebras, and Applications

- Contents vii8 free
- Introduction xi12 free
- History of the Great Plains Operator Theory Symposium xv16 free
- Applications, wavelets, dynamics, and quantum theory 120 free
- Operator theory and harmonic analysis 7594
- Non-commutative geometry 129148
- C*-algebras 163182
- Certain representations of the Cuntz relations, and a question on wavelets decompositions 165184
- The Rokhlin property for automorphisms on simple C*-algebras 189208
- Some recent topics on C*-algebras and related problems 217236
- Strong shift equivalence in the C*-algebraic setting: Graphs and C*-correspondences 221240
- Topological higher-rank graphs and the C*-algebras of topological 1-graphs 231250

- Von Neumann algebras 245264
- Frames in Hilbert space 273292
- The Kadison-Singer conjecture 297316
- Extensions and dilations 357376
- Multivariable operator theory 397416