Operator Algebras and Quantum Statistical Mechanics
by Ola Bratteli, Derek W. Robinson
Publisher: Springer 2003
Number of pages: 505
These two volumes present the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis.
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by John Erdos - King's College London
These are notes for a King's College course to fourth year undergraduates and MSc students. They cover the theoretical development of operators on Hilbert space up to the spectral theorem for bounded selfadjoint operators.
by W W L Chen - Macquarie University
An introduction to the basic ideas in linear functional analysis: metric spaces; connectedness, completeness and compactness; normed vector spaces; inner product spaces; orthogonal expansions; linear functionals; linear transformations; etc.
by Vaughan F. R. Jones - UC Berkeley Mathematics
The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. The philosophy is to lavish attention on a few key results and examples.
by Ivan F. Wilde - King's College, London
These notes are based on lectures given as part of a mathematics MSc program. The approach here is to discuss topological vector spaces - with normed spaces considered as special cases. Contents: Topological Spaces; Nets; Product Spaces; etc.