Classical analysis on normed spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1995
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 356 S. |
| ISBN: | 9810221371 |
Staff View
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Record in the Search Index
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| adam_text | CLASSICAL ANALYSIS ON NORMED SPACES TSOY-WO MA DEPARTMENT OF MATHEMATICS
UNIVERSITY OF WESTERN AUSTRALIA WORLD SCIENTIFIC SINGAPORE * NEW JERSEY
* LONDON * HONG KONG TABLE OF CONTENTS PREFACE VII INTRODUCTION XIII
CHAPTER 1, METRIC SPACES 1-1. STANDARD FINITE DIMENSIONAL VECTOR SPACES
1 1-2. CONVERGENT SEQUENCES IN METRIC SPACES 3 1-3. CONTINUOUS MAPS 5
1-4. OPEN SETS 7 1-5. CLOSURES OF SETS 9 1-6. CHARACTERIZATION OF
CONTINUITY 11 1-7. DUALITY OF CLOSURE-INTERIOR OPERATORS 13 1-8.
PARTITION OF UNITY 14 CHAPTER 2, COMPLETE, COMPACT AND CONNECTED SETS
2-1. CAUCHY SEQUENCES 18 2-2. BOUNDED SETS 19 2-3. UPPER AND LOWER
LIMITS 20 2-4. COMPLETE SETS 22 2-5. PRECOMPACT SETS 25 2-6. COMPACTNESS
27 2-7. CONTINUOUS MAPS ON COMPACT SPACES 30 2-8. UNIFORM CONTINUITY 32
2-9. CONNECTED SETS 34 2-10. COMPONENTS 37 CHAPTER 3, BANACH SPACES 3-1.
UNIFORM CONVERGENCE 40 3-2. BOUNDED CONTINUOUS FUNCTIONS 41 3-3.
SEQUENCE SPACES 44 3-4. CONTINUOUS LINEAR MAPS 48 3-5. EXAMPLES OF
CONTINUOUS LINEAR MAPS 51 3-6. FINITE DIMENSIONAL NORMED SPACES 55 3-7.
INFINITE DIMENSIONAL COMPACT SETS 57 3-8. APPROXIMATION IN FUNCTION
SPACES 61 TABLE OF CONTENTS CHAPTER 4, SIMPLICIAL COMPLEXES 4-1.
GEOMETRICALLY INDEPENDENT SETS 65 4-2. CONVEX SETS IN NORMED SPACES 69
4-3. SIMPLEXES 71 4-4. AFFINE MAPS 73 4-5. SIMPLICIAL COMPLEXES 75 4-6.
SMALL SIMPLEXES 78 4-7. BARYCENTRIC SUBDIVISIONS 80 4-8. SIMPLICIAL
APPROXIMATIONS 82 4-9. EXISTENCE OF SIMPLICIAL APPROXIMATIONS 85 4-10. A
COMBINATORIAL LEMMA WITH APPLICATION 86 CHAPTER 5, TOPOLOGICAL FIXED
POINTS 5-1. ANTIPODAL MAPS 91 5-2. RETRACTS AND FIXED POINTS 94 5-3.
FIXED POINTS OF COMPACT MAPS 97 5-4. COMPACT FIELDS AND THEIR HOMOTOPIES
99 5-5. EXTENSION PROPERTY 102 5-6. PROPERTIES OF COMPACT FIELDS IN
NORMED SPACES 106 CHAPTER 6, FOUNDATION OF FUNCTIONAL ANALYSIS 6-1.
TRANSFINITE INDUCTION ILL 6-2. HAHN-BANACH EXTENSION THEOREMS 113 6-3.
EXTENSION OF CONTINUOUS LINEAR FORMS 115 6-4. CLOSED HYPERPLANES 117
6-5. SEPARATION BY HYPERPLANES 120 6-6. EXTREME POINTS 122 6-7. BAIRE S
PROPERTY 124 6-8. UNIFORM BOUNDEDNESS 126 6-9. OPEN MAP AND CLOSED GRAPH
THEOREMS 128 CHAPTER 7, NATURAL CONSTRUCTION S 7-1. BIDUAL SPACES 131
7-2. QUOTIENT SPACES 134 7-3. DUALITY OF SUBSPACES AND QUOTIENTS 136
7-4. DIRECT SUMS 138 7-5. TRANSPOSES 141 TABLE OF CONTENTS XI 7-6.
REFLEXIVE SPACES 144 7-7. WEAK CONVERGENCE 146 7-8. WEAK-STAR
CONVERGENCE 149 CHAPTER 8, COMPLEX ANALYSIS 8-1. DERIVATIVES OF VECTOR
MAPS 151 8-2. INTEGRALS OF REGULATED MAPS 152 8-3. FUNDAMENTAL THEOREMS
OF CALCULUS 155 8-4. HOLOMORPHIC MAPS OF ONE COMPLEX VARIABLE 158 8-5.
SERIES EXPANSION 163 8-6. SPECTRUM 169 8-7. SPECTRAL RADIUS 173 8-8.
HOLOMORPHIC MAPS OF AN OPERATOR 175 CHAPTER 9, DIFFERENTIATION IN BANACH
SPACES 9-1. DIFFERENTIABLE MAPS 181 9-2. MEAN-VALUE THEOREM 185 9-3.
PARTIAL DERIVATIVES 188 9-4. FIXED POINTS OF CONTRACTIONS 193 9-5.
INVERSE AND IMPLICIT MAPPING THEOREMS 194 9-6. LOCAL PROPERTIES OF
DIFFERENTIABLE MAPS 199 CHAPTER 10, POLYNOMIALS AND HIGHER DERIVATIVES
10-1. MULTILINEAR MAPS ON BANACH SPACES 203 10-2. POLYNOMIALS ON BANACH
SPACES 206 10-3. HIGHER DERIVATIVES 211 10-4. C N -MAPS 214 10-5.
TAYLOR S EXPANSION 219 10-6. HIGHER CHAIN FORMULA AND HIGHER PRODUCT
FORMULA 224 CHAPTER 11, ORDINARY DIFFERENTIAL EQUATIONS 11-1. LOCAL
EXISTENCE AND UNIQUENESS 228 11-2. INTEGRAL CURVES 231 11-3. LINEAR
EQUATIONS 233 11-4. EXPONENTIAL FUNCTIONS OF MATRICES 238 11-5. GLOBAL
DEPENDENCE ON INITIAL CONDITIONS 242 11-6. SOLUTIONS WITHOUT UNIQUENESS
249 XII TABLE OF CONTENTS CHAPTER 12, COMPACT LINEAR OPERATORS 12-1.
BASIC PROPERTIES 253 12-2. RIESZ-SCHAUDER THEORY 257 12-3. SPECTRUM OF A
COMPACT OPERATOR 262 12-4. EXISTENCE OF INVARIANT SUBSPACES 263 CHAPTER
13, OPERATORS ON HILBERT SPACES 13-1. COMPLEX INNER PRODUCT SPACES 266
13-2. ORTHOGONALITY IN INNER PRODUCT SPACES 268 13-3. ORTHONORMAL BASES
OF HILBERT SPACES 271 13-4. ORTHOGONAL COMPLEMENTS 274 13-5. ADJOINTS
276 13-6. QUADRATIC FORMS : 280 13-7. NORMAL OPERATORS 282 13-8.
SELF-ADJOINT OPERATORS 284 13-9. PROJECTORS AND CLOSED VECTOR SUBSPACES
286 13-10. PARTIAL ORDER OF OPERATORS 290 13-11. EIGENVALUES 293 CHAPTER
14, SPECTRAL PROPERTIES OF HILBERT SPACES 14-1. SPECTRUM OF AN OPERATOR
295 14-2. APPROXIMATE SPECTRUM 296 -14-3. WEAK CONVERGENCE 299 14-4.
DIAGONAL OPERATORS 301 14-5. COMPACT OPERATORS 304 14-6. FUNCTIONAL
CALCULUS OF SELF-ADJOINT OPERATORS 310 14-7. POLAR DECOMPOSITION 315
CHAPTER 15, TENSOR PRODUCTS 15-1. ALGEBRAIC TENSOR PRODUCTS OF VECTOR
SPACES 318 15-2. TENSOR PRODUCTS OF LINEAR MAPS 320 15-3. INDEPENDENT
SETS IN TENSOR PRODUCTS 322 15-4. MATRIX REPRESENTATIONS 325 15-5.
PROJECTIVE NORMS ON TENSOR PRODUCTS 329 15-6. INDUCTIVE NORMS 334 15-7.
TENSOR PRODUCT OF HILBERT SPACES 337 REFERENCES 343 INDEX 351
|
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| author | Ma, Tsoy-Wo |
| author_facet | Ma, Tsoy-Wo |
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| author_sort | Ma, Tsoy-Wo |
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| building | Verbundindex |
| bvnumber | BV023763016 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)832658939 (DE-599)BVBBV023763016 |
| discipline | Mathematik |
| format | Book |
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| isbn | 9810221371 |
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| publisher | World Scientific |
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| spelling | Ma, Tsoy-Wo Verfasser aut Classical analysis on normed spaces Tsoy-Wo Ma Singapore [u.a.] World Scientific 1995 XVI, 356 S. txt rdacontent n rdamedia nc rdacarrier Normierter Raum (DE-588)4127735-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Normierter Raum (DE-588)4127735-1 s Analysis (DE-588)4001865-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017405259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ma, Tsoy-Wo Classical analysis on normed spaces Normierter Raum (DE-588)4127735-1 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4127735-1 (DE-588)4001865-9 |
| title | Classical analysis on normed spaces |
| title_auth | Classical analysis on normed spaces |
| title_exact_search | Classical analysis on normed spaces |
| title_full | Classical analysis on normed spaces Tsoy-Wo Ma |
| title_fullStr | Classical analysis on normed spaces Tsoy-Wo Ma |
| title_full_unstemmed | Classical analysis on normed spaces Tsoy-Wo Ma |
| title_short | Classical analysis on normed spaces |
| title_sort | classical analysis on normed spaces |
| topic | Normierter Raum (DE-588)4127735-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Normierter Raum Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017405259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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