Recent Advances in Operator Theory and Operator Algebras /
"This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent...
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| Format: | eBook |
| Language: | English |
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Boca Raton, FL :
CRC Press,
2017.
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| Edition: | First edition. |
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Half Title; Title; Copyright; Contents; Preface; Contributors; Chapter 1 Operator theory and Schubert calculus Hari Bercovici ; 1.1 Three questions in operator theory; 1.1.1 Sums of Hermitian matrices; 1.1.2 Products of matrices; 1.1.3 Jordan models; 1.2 Schubert calculus; 1.3 The Littlewood{Richardson rule; 1.4 Practical intersection theory; 1.5 Back to operators; 1.5.1 Sums of Hermitian matrices; 1.5.2 Products of matrices; 1.5.3 Jordan models; References; Chapter 2 Non-selfadjoint operator algebras: dynamics, classification and C*-envelopes E.G. Katsoulis ; 2.1 Introduction
- 2.2 Examples2.2.1 The semicrossed product C0(X) + ˙ Z; 2.2.2 The classi cation problem for semicrossed products; 2.2.3 The tensor algebra of a graph G; 2.3 C*-correspondences; 2.3.1 The gauge-invariance uniqueness theorems; 2.4 Adding tails to a C*-correspondence; 2.4.1 The Muhly{Tomforde tail; 2.4.2 The tail for (A; A; ); 2.5 The C*-envelope of an operator algebra; 2.5.1 The C*-envelope of an arbitrary operator algebra; 2.6 Dynamics and classification of operator algebras; 2.6.1 Piecewise conjugate multisystems; 2.6.2 The multivariable classi cation problem
- 2.7 Crossed products of operator algebras2.8 Local maps and representation theory; References; Chapter 3 An introduction to sofic entropy David Kerr ; 3.1 Introduction; 3.2 Internal and external approximation; 3.3 Amenable measure entropy; 3.4 Amenable topological entropy; 3.5 Sofic measure entropy; 3.6 Sofic topological entropy; 3.7 Dualizing sofic measure entropy; 3.8 Algebraic actions; 3.9 Further developments; References; Chapter 4 The solution of the Kadison-Singer problem Dan Timotin ; 4.1 Introduction; 4.2 The Kadison{Singer problem; 4.2.1 Pure states
- 4.2.2 The Kadison{Singer conjecture4.2.3 The paving conjecture; 4.3 Intermezzo: what we will do next and why; 4.3.1 General plan; 4.3.2 Sketch of the proof; 4.4 Analytic functions and univariate polynomials; 4.4.1 Preliminaries; 4.4.2 Nice families; 4.5 Several variables: real stable polynomials; 4.5.1 General facts; 4.5.2 The barrier function; 4.6 Characteristic and mixed characteristic polynomials; 4.6.1 Mixed characteristic polynomial; 4.6.2 Decomposing in rank one matrices and the characteris-tic polynomial; 4.7 Randomization; 4.7.1 Random matrices and determinants
- 4.7.2 Probability and partitions4.8 Proof of the paving conjecture ; 4.9 Final remarks; References; Index