An operator theory problem book:
Textbook for undergraduate college students and first year master's degree college students. In two parts, part 1 with exercises and part 2 with solutions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2019]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Textbook for undergraduate college students and first year master's degree college students. In two parts, part 1 with exercises and part 2 with solutions |
| Physical Description: | xvii, 637 Seiten |
| ISBN: | 9789813236257 9789813236271 |
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| 245 | 1 | 0 | |a An operator theory problem book |c Mohammed Hichem Mortad (University of Oran 1, Algeria) |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2019] | |
| 264 | 4 | |c © 2019 | |
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 520 | |a Textbook for undergraduate college students and first year master's degree college students. In two parts, part 1 with exercises and part 2 with solutions | ||
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Record in the Search Index
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| adam_text | Contents Preface xi Notation and Terminology 0.1. Notation 0.2. Terminology Part 1. xv xv xvi EXERCISES ET AL. 1 Chapter 1. Normed Vector Spaces. Banach Spaces 1.1. Basics 1.1.1. Definitions and Examples 1.1.2. Operations on Banach Spaces 1.1.3. Convex Sets 1.1.4. Lp-Spaces 1.2. True or False: Questions 1.3. Exercises with Solutions 1.4. Tests 1.5. More Exercises 3 3 3 11 13 14 18 19 22 23 Chapter 2. Bounded Linear Operators on Banach Spaces 2.1. Basics 2.1.1. Basic Definitions 2.1.2. Dual Spaces 2.1.3. The Fourier Transform 2.1.4. Invertibility 2.1.5. Series in Banach Spaces 2.1.6. Neumann Series 2.1.7. Operator-Valued AnalyticFunctions 2.1.8. The Four Pillars of Functional Analysis 2.2. True or False: Questions 2.3. Exercises with Solutions 2.4. Tests 2.5. More Exercises 25 25 25 34 36 38 40 44 46 47 52 52 62 63 V
Vi CONTENTS Chapter 3. Hilbert Spaces 67 3.1. Basics 67 3.1.1. Definitions and Examples 67 3.1.2. Modes of Convergence of Sequences 70 3.1.3. Orthogonality 72 3.1.4. The Closest Point Property and the Projection Theorem 74 3.1.5. Orthonormal Sets and Bases 75 3.1.6. Orthogonal Polynomials 78 3.1.7. Linear Operators on a Hilbert Space 79 3.1.8. Operator Topologies 84 3.2. True or False: Questions 86 3.3. Exercises with Solutions 87 3.4. Tests 96 3.5. More Exercises 96 Chapter 4. Classes of LinearOperators onHilbert Spaces 99 4.1. Basics 99 4.1.1. Operator Theory Basics 99 4.1.2. Cartesian Form 103 4.1.3. Operator Matrices 104 4.1.4. A Word on theInvariant Subspace Problem 108 4.2. True or False: Questions 113 4.3. Exercises with Solutions 113 4.4. Tests 120 4.5. More Exercises 120 Chapter 5. Positive Operators. Square Root 5.1. Basics 5.1.1. Positive Operators 5.1.2. Invertibility Revisited 5.1.3. Square Root of Positive Operators 5.2. True or False: Questions 5.3. Exercises with Solutions 5.4. Tests 5.5. More Exercises Chapter 6. 6.1. 6.1.1. 6.1.2. 6.1.3. 6.1.4. Absolute Value. Polar Decomposition of an Operator Basics Definitions and Properties The Absolute Value and the Product The Absolute Value and the Sum The Absolute Value and Other Inequalities 123 123 123 127 128 133 134 139 140 143 143 143 146 147 148
CONTENTS 6.1.5. 6.2. 6.3. 6.4. 6.5. Polar Decomposition True or False: Questions Exercises with Solutions Tests More Exercises vii 148 150 151 155 156 Chapter 7. Spectrum of an Operator 7.1. Basics 7.1.1. Definitions and Properties 7.1.2. The Resolvent Function 7.1.3. Subsets of the Spectrum 7.1.4. Spectrum of the Product of Operators 7.1.5. On The Operator Equation AX — XB = C 7.1.6. Polynomial Calculus 7.2. True or False: Questions 7.3. Exercises with Solutions 7.4. Tests 7.5. More Exercises 159 159 159 162 163 165 168 171 173 173 179 180 Chapter 8. Spectral Radius. Numerical Range 8.1. Basics 8.1.1. Spectral Radius 8.1.2. Numerical Range 8.2. True or False: Questions 8.3. Exercises with Solutions 8.4. Tests 8.5. More Exercises 183 183 183 185 187 188 190. 191 Chapter 9. Compact Operators 9.1. Basics 9.1.1. Compact Operators 9.1.2. Hilbert-Schmidt Operators 9.1.3. Spectrum and Compact Operators 9.2. True or False: Questions 9.3. Exercises with Solutions 9.4. Tests 9.5. More Exercises 193 193 193 195 197 198 199 202 203 Chapter 10. Closed Operators 10.1. Basics 10.1.1. Spectrum 10.1.2. Closedness of Productsand Sums 10.1.3. A Word onDistributionalDerivatives 207 207 211 212 213
CONTENTS viii 10.2. 10.3. 10.4. 10.5. True or False: Questions Exercises with Solutions Tests More Exercises 216 216 221 222 Chapter 11.1. 11.1.1. 11.1.2. 11.1.3. 11.1.4. 11.1.5. 11.2. 11.3. 11.4. 11.5. 11. Functional Calculi Basics Functional Calculus for Self-adjoint Operators Functional Calculus for Normal Operators A Little Digression The Fuglede-Putnam Theorem Revisited The Beck-Putnam Theorem True or False: Questions Exercises with Solutions Tests More Exercises Chapter 12.1. 12.2. 12.3. 12.4. 12.5. 12. Hyponormal Operators Basics True or False: Questions Exercises with Solutions Tests More Exercises 253 253 255 256 259 260 Chapter 13.1. 13.1.1. 13.1.2. 13.1.3. 13.2. 13.3. 13.4. 13. Similarities of Operators Important Theorems The Berberian Theorem The Williams Theorem The Embry Theorem Exercises with Solutions Tests More Exercises 261 261 261 261 262 262 265 265 Part 2. SOLUTIONS Chapter 1. Normed Vector Spaces. Banach Spaces 1.2. True or False: Answers 1.3. Solutions to Exercises 1.4. Hints/Answers to Tests 225 225 225 234 237 238 240 241 242 249 250 267 269 269 270 292 Chapter 2. Bounded Linear Operators on Banach Spaces 293 2.2. True or False: Answers 293 2.3. Solutions to Exercises 295 2.4. Hints/Answers to Tests 335
CONTENTS Chapter 3. Hilbert Spaces 3.2. True or False: Answers 3.3. Solutions to Exercises 3.4. Hints/Answers to Tests ix 337 337 339 375 Chapter 4. Classes of LinearOperators on Hilbert Spaces 377 4.2. True or False: Answers 377 4.3. Solutions to Exercises 379 4.4. Hints/Answers to Tests 405 Chapter 5. Positive Operators. Square Root 5.2. True or False: Answers 5.3. Solutions to Exercises 5.4. Hints/Answers to Tests Chapter 6. 6.2. 6.3. 6.4. Absolute Value. Polar Decomposition of an Operator True or False: Answers Solutions to Exercises Hints/Answers to Tests 407 407 409 431 433 433 434 449 Chapter 7. Spectrum of an Operator 7.2. True or False: Answers 7.3. Solutions to Exercises 7.4. Hints/Answers to Tests 453 453 454 484 Chapter 8. Spectral Radius. Numerical Range 8.2. True or False: Answers 8.3. Solutions to Exercises 8.4. Hints/Answers to Tests 487 487 489 499 Chapter 9. Compact Operators 9.2. True or False: Answers 9.3. Solutions to Exercises 9.4. Hints/Answers to Tests 501 501 502 527 Chapter 10.2. 10.3. 10.4. 10. Closed Operators True or False: Answers Solutions to Exercises Hints/Answers to Tests 529 529 530 556 Chapter 11.2. 11.3. 11.4. 11. Functional Calculi True or False: Answers Solutions to Exercises Hints/Answers to Tests 559 559 562 587
CONTENTS x Chapter 12.2. 12.3. 12.4. 12. Hyponormal Operators True or False: Answers Solutions to Exercises Hints/Answers to Tests 591 591 593 609 Chapter 13. Similarities of Operators 13.2. Solutions to Exercises 13.3. Hints/Answers to Tests 611 611 619 Bibliography 621 Index 633
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| isbn | 9789813236257 9789813236271 |
| language | English |
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| physical | xvii, 637 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | World Scientific |
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| spelling | Mortad, Mohammed Hichem 1978- (DE-588)1123528640 aut An operator theory problem book Mohammed Hichem Mortad (University of Oran 1, Algeria) New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2019] © 2019 xvii, 637 Seiten txt rdacontent n rdamedia nc rdacarrier Textbook for undergraduate college students and first year master's degree college students. In two parts, part 1 with exercises and part 2 with solutions Operator theory Textbooks Functional analysis Textbooks Operatortheorie (DE-588)4075665-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030451418&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mortad, Mohammed Hichem 1978- An operator theory problem book Operator theory Textbooks Functional analysis Textbooks Operatortheorie (DE-588)4075665-8 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4018916-8 |
| title | An operator theory problem book |
| title_auth | An operator theory problem book |
| title_exact_search | An operator theory problem book |
| title_full | An operator theory problem book Mohammed Hichem Mortad (University of Oran 1, Algeria) |
| title_fullStr | An operator theory problem book Mohammed Hichem Mortad (University of Oran 1, Algeria) |
| title_full_unstemmed | An operator theory problem book Mohammed Hichem Mortad (University of Oran 1, Algeria) |
| title_short | An operator theory problem book |
| title_sort | an operator theory problem book |
| topic | Operator theory Textbooks Functional analysis Textbooks Operatortheorie (DE-588)4075665-8 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Operator theory Textbooks Functional analysis Textbooks Operatortheorie Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030451418&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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