Summability Through Functional Analysis

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Elsevier, Apr 1, 2000 - Mathematics - 317 pages
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Summability is an extremely fruitful area for the application of functional analysis; this volume could be used as a source for such applications. Those parts of summability which only have ``hard'' (classical) proofs are omitted; the theorems given all have ``soft'' (functional analytic) proofs.

 

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Contents

CHAPTER 1 MATRICES
1
CHAPTER 2 CLASSICAL MATRICES
21
CHAPTER 3 TRIANGLES AND BANACH SPACE
39
CHAPTER 4 FK SPACES
51
CHAPTER 5 REPLACEABILITY AND CONSISTENCY
75
CHAPTER 6 BIGNESS THEOREMS
89
CHAPTER 7 SEQUENCE SPACES
103
CHAPTER 8 INCLUSION AND MAPPING
115
CHAPTER 12 DISTINGUISHED SUBSPACES OF MATRIX DOMAINS
187
CHAPTER 13 DISTINGUISHED SUBSPACES OF cA
201
CHAPTER 14 THE FUNCTIONAL μ
221
CHAPTER 15 THE SUBSPACE P
233
CHAPTER 16 SEQUENTIAL COMPLETENESS AND SEPARABILITY
251
CHAPTER 17 MAPS OF BANACH SPACES
263
CHAPTER 18 ALGEBRA
281
CHAPTER 19 MISCELLANY
291

CHAPTER 9 SEMICONSERVATIVE SPACES AND MATRICES
141
CHAPTER 10 DISTINGUISHED SUBSPACES OF FK SPACES
157
CHAPTER 11 EXTENSION
179
BIBLIOGRAPHY
303
INDEX
309
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