Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanics
by N.P. Landsman
Publisher: arXiv 1998
Number of pages: 90
This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space localization. The reader is supposed to know elementary functional analysis and quantum mechanics.
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by Vladimir V. Kisil - University of Leeds
Contents: Fourier Series; Basics of Linear Spaces; Orthogonality; Fourier Analysis; Duality of Linear Spaces; Operators; Spectral Theory; Compactness; The spectral theorem for compact normal operators; Applications to integral equations; etc.
by Harald Hanche-Olsen, Erling Størmer - Pitman
Introduction to Jordan algebras of operators on Hilbert spaces and their abstract counterparts. It develops the theory of Jordan operator algebras to a point from which the theory of C*- and von Neumann algebras can be generalized to Jordan algebras.
by Peter W. Michor - Springer
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
by Gerald Teschl - Universitaet Wien
This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.