A Course in functional analysis

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Başlık:

Yazar:

Conway, John B.

ISBN:

9780387972459

Ek Yazar:

Conway, John B.

Basım Bilgisi:

2nd ed.

Yayın Bilgisi:

New York : Springer - Verlag , 1990.

Fiziksel Tanım:

XVI, 399 s. ; 24 sm.

Seriler:

Graduate texts in mathematics ; 96

Seri Başlığı:

Graduate texts in mathematics ; 96

Genel Not:

Includes bibliographical references

Özet:

Graduate texts in Mathematics John B. Conway Contents Preface vii Preface to the Second Edition xi CHAPTERI Hubert Spaces §1. Elementary Properties and Examples 1 §2. Orthogonality 7 §3. The Riesz Representation Theorem 11 §4. Orthonormal Sets of Vectors and Bases 14 §5. Isomorphic Hubert Spaces and the Fqurier Transform for the Circle 19 §6. The Direct Sum of Hubert Spaces 23 CHAPTER II Operators on Hubert Space §1. Elementary Properties and Examples 26 §2. The Adjoint of an Operator 31 §3. Projections and Idempotents; Invariant and Reducing Subspaces 36 §4. Compact Operators 41 §5.* The Diagonalization of Compact Self-Adjoint Operators 46 §6.* An Application: Sturm-Liouville Systems 49 §7.* The Spectral Theorem and Functional Calculus for Compact Normal Operators 54 §8.* Unitary Equivalence for Compact Normal Operators 60 CHAPTER III Banach Spaces §1. Elementary Properties and Examples 63 §2. Linear Operators on Normed Spaces 67 §3. Finite Dimensional Normed Spaces 69 §4. Quotients and Products of Normed Spaces 70 §5. Linear Functionals 73 §6. The Hahn-Banach Theorem 77 §7.* An Application: Banach Limits 82 §8.* An Application: Runge’s Theorem 83 §9.* An Application: Ordered Vector Spaces 86 §10. The Dual of a Quotient Space and a Subspace 88 §11. Reflexive Spaces 89 §12. The Open Mapping and Closed Graph Theorems 90 §13. Complemented Subspaces of a Banach Space 93 §14. The Principle of Uniform Boundedness 95 CHAPTER IV Locally Convex Spaces §1. Elementary Properties and Examples 99 §2. Metrizable and Normable Locally Convex Spaces 105 §3. Some Geometric Consequences of the Hahn-Banach Theorem 108 §4.* Some Examples of the Dual Space of a Locally Convex Space 114 §5.* Inductive Limits and the Space of Distributions 116 CHAPTER V Weak Topologies §1. Duality 124 §2. The Dual of a Subspace and a Quotient Space 128 §3. Alaoglu’s Theorem 130 §4. Reflexivity Revisited 131 §5. Separability and Metrizability 134 §6.* An Application: The Stone-Ğech Compactification 137 §7. The Krein-Milman Theorem 141 §8. An Application: The Stone-Weierstrass Theorem 145 §9.* The Schauder Fixed Point Theorem 149 §10.* The Ryll-Nardzewski Fixed Point Theorem 151 §11.* An Application: Haar Measure on a Compact Group 154 §12.* The Krein-Smulian Theorem 159 §13.* Weak Compactness 163 CHAPTER VI Linear Operators on a Banach Space §1. The Adjoint of a Linear Operator 166 §2.* The Banach-Stone Theorem 171 §3. Compact Operators 173 §4. Invariant Subspaces 178 §5. Weakly Compact Operators 183 HAPTER VII anach Algebras and Spectral Theory for perators on a Banach Space 1. Elementary Properties and Examples 187 2. Ideals and Quotients 191 3. The Spectrum 195 4. The Riesz Functional Calculus 199 5. Dependence of the Spectrum on the Algebra 205 6. The Spectrum of a Linear Operator 208 7. The Spectral Theory of a Compact Operator 214 8. Abelian Banach Algebras 218 9.* The Group Algebra of a Locally Compact Abelian Group 223 HAPTER VIII "-Algebras ’’-’ 1. Elementary Properties and Examples 232 2. Abelian C*-Algebras and the Functional Calculus in C*-Algebras 236 3. The Positive Elements in a C*-Algebra 240 4.* Ideals and Quotients of C*-Algebras 245 5.* Representations of C*-Algebras and the Gelfand-Naimark-Segal Construction 248 HAPTER IX ormal Operators on Hubert Space 1. Spectral Measures and Representations of Abelian C*-Algebras 255 2. The Spectral Theorem 262 3. Star-Cyclic Normal Operators 268 4. Some Applications of the Spectral Theprem 271 5. Topologies on 3S(tf) 274 6. Commuting Operators 276 7. Abelian von Neumann Algebras 281 8. The Functional Calculus for Normal Operators: The Conclusion of the Saga 285 9. Invariant Subspaces for Normal Operators 290 0. Multiplicity Theory for Normal Operators: A Complete Set of Unitary Invariants 293 HAPTER X nbounded Operators il. Basic Properties and Examples 303 >2. Symmetric and Self-Adjoint Operators 308 ’3. The Cayley Transform 316 4. Unbounded Normal Operators and the Spectral Theorem 319 ;5. Stone’s Theorem 327 >6. The Fourier Transform and Differentiation 334 >7. Moments 343 CHAPTER XI Fredholm Theory §1. The Spectrum Revisited 347 §2. Fredholm Operators 349 §3. The Fredholm Index 352 §4. The Essential Spectrum 358 §5. The Components of y& 362 §6. A Finer Analysis of the Spectrum 363 APPENDIX A Preliminaries §1. Linear Algebra 369 §2. Topology 371 APENDIX B The Dual of U(^i) 375 APPENDIX C The Dual of C0(X) 378 Bibliography 384 List of Symbols 391 Index l 395

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Library	Materyal Türü	Barkod	Yer Numarası	Durumu/İade Tarihi
Arıyor... Ferit Melen Library	Book	049584	515.7 CONc 1990 k.2	Arıyor... Unknown

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