Elementary Operator Theory / / Marat V. Markin.
The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and...
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Markin, Marat V., author. aut http://id.loc.gov/vocabulary/relators/aut Elementary Operator Theory / Marat V. Markin. Berlin ; Boston : De Gruyter, [2020] ©2020 1 online resource (XV, 410 p.) : ca. 2000 Formeln text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Preface -- Contents -- 1 Preliminaries -- 2 Metric Spaces -- 3 Vector Spaces, Normed Vector Spaces, and Banach Spaces -- 4 Linear Operators -- 5 Elements of Spectral Theory in a Banach Space Setting -- 6 Elements of Spectral Theory in a Hilbert Space Setting -- A The Axiom of Choice and Equivalents -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental principles (the Uniform Boundedness Principle and the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems), to the elements of the spectral theory, including Gelfand's Spectral Radius Theorem and the Spectral Theorem for Compact Self-Adjoint Operators, and its applications, such as the celebrated Lyapunov Stability Theorem. Conceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. ContentsPreface PreliminariesMetric SpacesVector Spaces, Normed Vector Spaces, and Banach SpacesLinear OperatorsElements of Spectral Theory in a Banach Space SettingElements of Spectral Theory in a Hilbert Space SettingAppendix: The Axiom of Choice and Equivalents BibliographyIndex Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Jan 2023) Banach-Raum. Hilbert-Raum. Metrischer Raum. Operatortheorie. Spektraltheorie. MATHEMATICS / Functional Analysis. bisacsh Title is part of eBook package: De Gruyter DG Ebook Package English 2020 9783110696288 Title is part of eBook package: De Gruyter DG Plus DeG Package 2020 Part 1 9783110696271 Title is part of eBook package: De Gruyter De Gruyter English eBooks 2020 - UC 9783110659061 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English 9783110704716 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 9783110704518 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 English 9783110704846 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 9783110704662 ZDB-23-DMA EPUB 9783110598889 print 9783110600964 https://doi.org/10.1515/9783110600988 https://www.degruyter.com/isbn/9783110600988 Cover https://www.degruyter.com/document/cover/isbn/9783110600988/original |
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English |
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author |
Markin, Marat V., Markin, Marat V., |
spellingShingle |
Markin, Marat V., Markin, Marat V., Elementary Operator Theory / De Gruyter Textbook Frontmatter -- Preface -- Contents -- 1 Preliminaries -- 2 Metric Spaces -- 3 Vector Spaces, Normed Vector Spaces, and Banach Spaces -- 4 Linear Operators -- 5 Elements of Spectral Theory in a Banach Space Setting -- 6 Elements of Spectral Theory in a Hilbert Space Setting -- A The Axiom of Choice and Equivalents -- Bibliography -- Index |
author_facet |
Markin, Marat V., Markin, Marat V., |
author_variant |
m v m mv mvm m v m mv mvm |
author_role |
VerfasserIn VerfasserIn |
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Markin, Marat V., |
title |
Elementary Operator Theory / |
title_full |
Elementary Operator Theory / Marat V. Markin. |
title_fullStr |
Elementary Operator Theory / Marat V. Markin. |
title_full_unstemmed |
Elementary Operator Theory / Marat V. Markin. |
title_auth |
Elementary Operator Theory / |
title_alt |
Frontmatter -- Preface -- Contents -- 1 Preliminaries -- 2 Metric Spaces -- 3 Vector Spaces, Normed Vector Spaces, and Banach Spaces -- 4 Linear Operators -- 5 Elements of Spectral Theory in a Banach Space Setting -- 6 Elements of Spectral Theory in a Hilbert Space Setting -- A The Axiom of Choice and Equivalents -- Bibliography -- Index |
title_new |
Elementary Operator Theory / |
title_sort |
elementary operator theory / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2020 |
physical |
1 online resource (XV, 410 p.) : ca. 2000 Formeln Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- 1 Preliminaries -- 2 Metric Spaces -- 3 Vector Spaces, Normed Vector Spaces, and Banach Spaces -- 4 Linear Operators -- 5 Elements of Spectral Theory in a Banach Space Setting -- 6 Elements of Spectral Theory in a Hilbert Space Setting -- A The Axiom of Choice and Equivalents -- Bibliography -- Index |
isbn |
9783110600988 9783110696288 9783110696271 9783110659061 9783110704716 9783110704518 9783110704846 9783110704662 9783110598889 9783110600964 |
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https://doi.org/10.1515/9783110600988 https://www.degruyter.com/isbn/9783110600988 https://www.degruyter.com/document/cover/isbn/9783110600988/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110600988 |
oclc_num |
1149462702 |
work_keys_str_mv |
AT markinmaratv elementaryoperatortheory |
status_str |
n |
ids_txt_mv |
(DE-B1597)494859 (OCoLC)1149462702 |
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Title is part of eBook package: De Gruyter DG Ebook Package English 2020 Title is part of eBook package: De Gruyter DG Plus DeG Package 2020 Part 1 Title is part of eBook package: De Gruyter De Gruyter English eBooks 2020 - UC Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 |
is_hierarchy_title |
Elementary Operator Theory / |
container_title |
Title is part of eBook package: De Gruyter DG Ebook Package English 2020 |
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1770177714786926592 |
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