Global Analysis: Functional Analysis Examples
by Leif Mejlbro
Publisher: BookBoon 2009
Number of pages: 78
From the table of contents: Metric spaces; Topology; Continuous mappings; Sequences; Semi-continuity; Connected sets, differentiation; Addition and multiplication by scalars in normed vector spaces; Normed vector spaces and integral operators; Differentiable mappings; Complete metric spaces; and more.
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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 - 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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The book is concerned with the application of a variety of methods to both non-linear (fixed point) problems and linear (eigenvalue) problems in infinite dimensional spaces. Author was interested in the construction of eigenvectors and eigenvalues.
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This book is the final outgrowth of a sequence of seminars about functors on categories of Banach spaces (held 1971 - 1975) and several doctoral dissertations. It has been written for readers with a general background in functional analysis.