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An invitation to operator theory:

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Bibliographische Detailangaben
Beteiligte Personen:	Abramovich, Yuri A. 1945-2003 (VerfasserIn), Aliprantis, Charalambos D. 1946-2009 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Providence, RI American Math. Soc. 2002
Schriftenreihe:	Graduate studies in mathematics 50
Schlagwörter:	Análise funcional Opérateurs, Théorie des Álgebras de operadores Operator theory Operatortheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIV, 530 S. graph. Darst.
ISBN:	0821821466 9780821821466

Internformat

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Datensatz im Suchindex

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adam_text	Contents Foreword ix Chapter 1. Odds and Ends 1 Â§1.1. Banach Spaces, Operators, and Linear Functional 1 Â§1.2. Banach Lattices and Positive Operators 13 Â§1.3. Bases in Banach Spaces 27 Â§1.4. Ultrapowers of Banach Spaces 37 Â§1.5. Vector valued Functions 44 Â§1.6. Fundamentals of Measure Theory 52 Chapter 2. Basic Operator Theory 69 Â§2.1. Bounded Below Operators 69 Â§2.2. The Ascent and Descent of an Operator 79 Â§2.3. Banach Lattices with Order Continuous Norms 84 Â§2.4. Compact and Weakly Compact Positive Operators 88 Chapter 3. Operators on AL and AM spaces 93 Â§3.1. AL and AM spaces 94 Â§3.2. Complex Banach Lattices 103 Â§3.3. The Center of a Banach Lattice 112 Â§3.4. The Predual of a Principal Ideal 119 Chapter 4. Special Classes of Operators 123 Â§4.1. Finite rank Operators 123 Â§4.2. Multiplication Operators 135 v vi Contents Â§4.3. Lattice and Algebraic Homomorphisms 142 Â§4.4. Fredholm Operators 155 Â§4.5. Strictly Singular Operators 170 Chapter 5. Integral Operators 179 Â§5.1. The Basics of Integral Operators 180 Â§5.2. Abstract Integral Operators 193 Â§5.3. Conditional Expectations and Positive Projections 211 Â§5.4. Positive Projections and Lattice subspaces 228 Chapter 6. Spectral Properties 237 Â§6.1. The Spectrum of an Operator 237 Â§6.2. Special Points of the Spectrum 248 Â§6.3. The Resolvent of a Positive Operator 253 Â§6.4. Functional Calculus 256 Chapter 7. Some Special Spectra 271 Â§7.1. The Spectrum of a Compact Operator 272 Â§7.2. Turning Approximate Eigenvalues into Eigenvalues 281 Â§7.3. The Spectrum of a Lattice Homomorphism 287 Â§7.4. The Order Spectrum of an Order Bounded Operator 291 Â§7.5. The Essential Spectrum of a Bounded Operator 298 Chapter 8. Positive Matrices 315 Â§8.1. The Banach Lattices Mn(R) and Mn(C) 316 Â§8.2. Operators on Finite Dimensional Spaces 320 Â§8.3. Matrices with Non negative Entries 329 Â§8.4. Irreducible Matrices 332 Â§8.5. The Perron Frobenius Theorem 339 Chapter 9. Irreducible Operators 347 Â§9.1. Irreducible and Expanding Operators 347 Â§9.2. Ideal Irreducibility and the Spectral Radius 357 Â§9.3. Band Irreducibility and the Spectral Radius 365 Â§9.4. Krein Operators on C(Q) spaces 370 Chapter 10. Invariant Subspaces 381 Â§10.1. A Smorgasbord of Invariant Subspaces 383 Â§10.2. The Lomonosov Invariant Subspace Theorem 393 Contents vii Â§10.3. Invariant Ideals for Positive Operators 398 Â§10.4. Invariant Subspaces of Families of Positive Operators 409 Â§10.5. Compact friendly Operators 425 Â§10.6. Positive Operators on Banach Spaces with Bases 436 Â§10.7. A Characterization of Non transitive Algebras 440 Â§10.8. Comments on the Invariant Subspace Problem 449 Chapter 11. The Daugavet Equation 455 Â§11.1. The Daugavet Equation and Uniform Convexity 456 Â§11.2. The Daugavet Property in AL and vlM spaces 467 Â§11.3. The Daugavet Property in Banach Spaces 471 Â§11.4. The Daugavet Property in C(fi) spaces 477 Â§11.5. Slices and the Daugavet Property 487 Â§11.6. Narrow Operators 493 Â§11.7. Some Applications of the Daugavet Equation 500 Bibliography 505 Index 521
any_adam_object	1
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dewey-tens	510 - Mathematics
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series	Graduate studies in mathematics
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spellingShingle	Abramovich, Yuri A. 1945-2003 Aliprantis, Charalambos D. 1946-2009 An invitation to operator theory Graduate studies in mathematics Análise funcional larpcal Opérateurs, Théorie des Álgebras de operadores larpcal Operator theory Operatortheorie (DE-588)4075665-8 gnd
subject_GND	(DE-588)4075665-8
title	An invitation to operator theory
title_auth	An invitation to operator theory
title_exact_search	An invitation to operator theory
title_full	An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis
title_fullStr	An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis
title_full_unstemmed	An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis
title_short	An invitation to operator theory
title_sort	an invitation to operator theory
topic	Análise funcional larpcal Opérateurs, Théorie des Álgebras de operadores larpcal Operator theory Operatortheorie (DE-588)4075665-8 gnd
topic_facet	Análise funcional Opérateurs, Théorie des Álgebras de operadores Operator theory Operatortheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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