UID:
almahu_9949697958502882
Format:
1 online resource (235 p.)
ISBN:
1-281-79356-6
,
9786611793562
,
0-08-087136-4
Series Statement:
North-Holland mathematics studies ; 25
Content:
Approximation of vector valued functions
Note:
Description based upon print version of record.
,
Front Cover; Approximation of Vector Valued Functions; Copyright Page; CONTENTS; PREFACE; INTRODUCTION; CHAPTER 1. THE COMPACT-OPEN TOPOLOGY; 1. Basic definitions; 2. Localizability; 3. Preliminary lemmas; 4. Stone-Weierstrass Theorem for modules; 5. The complex self -adjoint case; 6. Submodules of C (X; E); 7. An example: a theorem of Rudin; 8. Bishop's Theorem; 9. Vector fibrations; 10. Extreme functionals; 11. Representation of vector fibrations; 12. The approximation property; Appendix. Non-locally convex spaces; CHAPTER 2. THE THEOREM OF DIEUDONNE
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CHAPTER 3. EXTENSION THEOREMSCHAPTER 4. POLYNOMIAL ALGEBRAS; 1. Basic definitions and lemmas; 2. Stone-Weierstrass subspaces; 3. C(x)-modules; 4. Approximation of compact operators; CHAPTER 5. WEIGHTED APPROXIMATION; 1. Definition of Nachbin spaces; 2. The Bernstein-Nachbin approximation problem; 3. Sufficient conditions for sharp localizability; 4. Completeness o f Nachbin spaces; 5. Dual spaces of Nachbin spaces; Appendix. Fundamental weights; CHAPTER 6. THE SPACE Co (X; E) with the uniform topology; CHAPTER 7. THE SPACE Cb ( X; E) with the strict topology
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CHAPTER 8. THE e-PRODUCT OF L. SCHWARTZ 1. General definitions; 2. Spaces of continuous functions; 3. The approximation property; 4. Mergelyan's Theorem; 5. Localiz ation of the approximation property; CHAPTER 9. NONARCHIMEDEAN APPROXIMATION THEORY; 1. Valued fields; 2. Kaplansky's Theorem; 3. Normed spaces; 4. Vector-valued functions; 5. Vector fibrations; 6. Some applications; 7. Bishop's Theorem; 8. Tietze Extension Theorem; 9. The compact-open topology; 10. The nonarchimedean strict topology; BIBLIOGRAPHY; SYMBOL INDEX; INDEX
,
English
Additional Edition:
ISBN 0-444-85030-9
Language:
English
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