東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Counterexamples in operator theory

Mortad, Mohammed Hichem.

FindBook

Google Book

Amazon

博客來

Counterexamples in operator theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Counterexamples in operator theory/ by Mohammed Hichem Mortad.
作者:	Mortad, Mohammed Hichem.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xxxvi, 598 p. :ill., digital ;24 cm.
內容註:	Preface -- Part 1. Bounded Linear Operators -- Some Basic Properties -- Basic Classes of Bounded Linear Operators -- Operator Topologies -- Positive Operators -- Matrices of Bounded Operators -- (Square) Roots of Bounded Operators -- Absolute Value. Polar Decomposition -- Spectrum -- Spectral Radius. Numerical Range -- Compact Operators -- Functional Calculi -- Fuglede-Putnam Theorems and Intertwining Relations -- Operator Exponentials -- Nonnormal Operators -- Similarity and Unitary Equivalence -- The Sylvester Equation -- More Questions and Some Open Problems -- Part 2. Unbounded Linear Operators -- Basic Notions -- Closedness -- Adjoints. Symmetric Operators -- Self-adjointness -- (Arbitrary) Square Roots -- Normality -- Absolute Value. Polar Decomposition -- Unbounded Nonnormal Operators -- Commutativity -- The Fuglede-Putnam Theorems and Intertwining Relations -- Commutators -- Spectrum -- Matrices of Unbounded Operators -- Relative Boundedness -- More Questions and Some Open Problems II -- Appendix A: A Quick Review of the Fourier Transform -- Appendix B: A Word on Distributions and Sobolev Spaces -- Bibliography -- Index.
Contained By:	Springer Nature eBook
標題:	Operator theory. -
電子資源:	https://doi.org/10.1007/978-3-030-97814-3
ISBN:	9783030978143

Counterexamples in operator theory
Mortad, Mohammed Hichem.

Counterexamples in operator theory[electronic resource] /by Mohammed Hichem Mortad. - Cham :Springer International Publishing :2022. - xxxvi, 598 p. :ill., digital ;24 cm.

Preface -- Part 1. Bounded Linear Operators -- Some Basic Properties -- Basic Classes of Bounded Linear Operators -- Operator Topologies -- Positive Operators -- Matrices of Bounded Operators -- (Square) Roots of Bounded Operators -- Absolute Value. Polar Decomposition -- Spectrum -- Spectral Radius. Numerical Range -- Compact Operators -- Functional Calculi -- Fuglede-Putnam Theorems and Intertwining Relations -- Operator Exponentials -- Nonnormal Operators -- Similarity and Unitary Equivalence -- The Sylvester Equation -- More Questions and Some Open Problems -- Part 2. Unbounded Linear Operators -- Basic Notions -- Closedness -- Adjoints. Symmetric Operators -- Self-adjointness -- (Arbitrary) Square Roots -- Normality -- Absolute Value. Polar Decomposition -- Unbounded Nonnormal Operators -- Commutativity -- The Fuglede-Putnam Theorems and Intertwining Relations -- Commutators -- Spectrum -- Matrices of Unbounded Operators -- Relative Boundedness -- More Questions and Some Open Problems II -- Appendix A: A Quick Review of the Fourier Transform -- Appendix B: A Word on Distributions and Sobolev Spaces -- Bibliography -- Index.

This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students. The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief "Basics" section for the readers' reference, and many of the counterexamples included are the author's original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference.

ISBN: 9783030978143

Standard No.: 10.1007/978-3-030-97814-3doiSubjects--Topical Terms:

542531
Operator theory.

LC Class. No.: QA329

Dewey Class. No.: 515.724

Counterexamples in operator theory
LDR:03522nmm a2200325 a 4500 001 2300692
003 DE-He213
005 20220503161159.0
006 m d
007 cr nn 008maaau
008 230324s2022 sz s 0 eng d
020 $a 9783030978143 $q (electronic bk.)
020 $a 9783030978136 $q (paper)
024 7 $a 10.1007/978-3-030-97814-3 $2 doi
035 $a 978-3-030-97814-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA329
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.724 $2 23
090 $a QA329 $b .M887 2022
100 1 $a Mortad, Mohammed Hichem. $3 3599443
245 1 0 $a Counterexamples in operator theory $h [electronic resource] / $c by Mohammed Hichem Mortad.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2022.
300 $a xxxvi, 598 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- Part 1. Bounded Linear Operators -- Some Basic Properties -- Basic Classes of Bounded Linear Operators -- Operator Topologies -- Positive Operators -- Matrices of Bounded Operators -- (Square) Roots of Bounded Operators -- Absolute Value. Polar Decomposition -- Spectrum -- Spectral Radius. Numerical Range -- Compact Operators -- Functional Calculi -- Fuglede-Putnam Theorems and Intertwining Relations -- Operator Exponentials -- Nonnormal Operators -- Similarity and Unitary Equivalence -- The Sylvester Equation -- More Questions and Some Open Problems -- Part 2. Unbounded Linear Operators -- Basic Notions -- Closedness -- Adjoints. Symmetric Operators -- Self-adjointness -- (Arbitrary) Square Roots -- Normality -- Absolute Value. Polar Decomposition -- Unbounded Nonnormal Operators -- Commutativity -- The Fuglede-Putnam Theorems and Intertwining Relations -- Commutators -- Spectrum -- Matrices of Unbounded Operators -- Relative Boundedness -- More Questions and Some Open Problems II -- Appendix A: A Quick Review of the Fourier Transform -- Appendix B: A Word on Distributions and Sobolev Spaces -- Bibliography -- Index.
520 $a This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students. The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief "Basics" section for the readers' reference, and many of the counterexamples included are the author's original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference.
650 0 $a Operator theory. $3 542531
650 1 4 $a Operator Theory. $3 897311
650 2 4 $a Functional Analysis. $3 893943
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-97814-3
950 $a Mathematics and Statistics (SpringerNature-11649)