LEADER 04380nam 22005655 450 001 9910568266203321 005 20251113210907.0 010 $a9783030978143$b(electronic bk.) 010 $z9783030978136 024 7 $a10.1007/978-3-030-97814-3 035 $a(MiAaPQ)EBC6975908 035 $a(Au-PeEL)EBL6975908 035 $a(CKB)21957562800041 035 $a(PPN)269154965 035 $a(OCoLC)1319219251 035 $a(DE-He213)978-3-030-97814-3 035 $a(EXLCZ)9921957562800041 100 $a20220503d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCounterexamples in Operator Theory /$fby Mohammed Hichem Mortad 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2022. 215 $a1 online resource (613 pages) 225 1 $aMathematics and Statistics Series 311 08$aPrint version: Mortad, Mohammed Hichem Counterexamples in Operator Theory Cham : Springer International Publishing AG,c2022 9783030978136 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students. The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief ?Basics? section for the readers? reference, andmany of the counterexamples included are the author?s original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference. 410 0$aMathematics and Statistics Series 606 $aOperator theory 606 $aFunctional analysis 606 $aOperator Theory 606 $aFunctional Analysis 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aOperator Theory. 615 24$aFunctional Analysis. 676 $a515.724 676 $a515.724 700 $aMortad$b Mohammed Hichem$f1978-$01264582 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910568266203321 996 $aCounterexamples in operator theory$92965421 997 $aUNINA