A primer on Hilbert space theory : linear spaces, topological spaces, metric spaces, normed spaces, and topological groups / Carlo Alabiso, Ittay Weiss.

Format:

Book

Author/Creator:

Alabiso, Carlo.

Contributor:

Weiss, Ittay.

Series:

UNITEXT for physics

UNITEXT for Physics

Language:

English

Subjects (All):

Hilbert space.

Topological spaces.

Metric spaces.

Normed linear spaces.

Genre:

Electronic books.

Physical Description:

1 online resource (343 pages).

Edition:

Second edition.

Place of Publication:

Cham : Springer, 2021.

System Details:

text file

Summary:

This book offers an essential 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 providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authorss lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Contents:

1. Hilbert Space Theory - A Quick Overview

2. Linear Spaces

3. Topological Spaces

4. Metric Spaces

5. The Lebesgue Integral Following Mikusiniski

6. Banach Spaces

7. Hilbert Spaces

8. A Survery of mathematical structures related to Hilbert space theory

9. Solved Problems.

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed March 30, 2021).

Other Format:

Print version: Alabiso, Carlo A Primer on Hilbert Space Theory : Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups

ISBN:

9783030674175

3030674177

OCLC:

1241445668

Access Restriction:

Restricted for use by site license.