C*-algebraic Methods in Spectral Theory
by Serge Richard
Publisher: Nagoya University 2014
Number of pages: 103
From the table of contents: Linear operators on a Hilbert space; C*-algebras; Crossed product C*-algebras; Schroedinger operators and essential spectrum; Twisted crossed product C*-algebras; Pseudodifferential calculus; Magnetic systems.
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by D. Husemoller - Tata Institute of Fundamental Research
Contents: Exact Couples and the Connes Exact Couple; Abelianization and Hochschild Homology; Cyclic Homology and the Connes Exact Couple; Cyclic Homology and Lie Algebra Homology; Mixed Complexes, the Connes Operator B; and more.
by Gerald Teschl - University of Vienna
This free manuscript provides a brief introduction to Functional Analysis. The text covers basic Hilbert and Banach space theory including Lebesgue spaces and their duals (no knowledge about Lebesgue integration is assumed).
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Notes from a course which covered themes in functional analysis and operator theory, with an emphasis on topics of special relevance to such applications as representation theory, harmonic analysis, mathematical physics, and stochastic integration.
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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.