A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, And Topological Group: Linear Spac by Carlo AlabisoA Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, And Topological Group: Linear Spac by Carlo Alabiso

A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces…

byCarlo Alabiso, Ittay Weiss

Hardcover | October 20, 2014

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This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude.

With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Prof. Carlo Alabiso obtained his Degree in Physics at Milan University and then taught at Parma University, Parma, Italy for more than 40 years (with a period spent as a research fellow at the Stanford Linear Accelerator Center and at Cern, Geneva). His teaching encompassed topics in quantum mechanics, special relativity, field theory,...
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Title:A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces…Format:HardcoverDimensions:255 pagesPublished:October 20, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319037129

ISBN - 13:9783319037127

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Table of Contents

1 Introduction and Preliminaries.- 2 Linear Spaces.- 3 Topological Spaces.- 4 Metric Spaces.- 5 Normed Spaces.- 6 Topological Groups.- 7 Solved Problems.

Editorial Reviews

"This book introduces essential ideas and results of Hilbert space and linear operator theory to beginners in quantum physics. . The textbook is suitable for advanced undergraduate or introductory graduate courses for both physics and mathematics students." (Michael Frank, Mathematical Reviews, August, 2015)