Summability Through Functional Analysis (North-holland Mathematics Studies)

c o n s e r v a t i v e B 3 B ( c ) ( 1 0 . 2 . 9 ) = E m , so any bounded sequence is i n P (Theorem 3 ) . (The more g e n e r a l assumption A c 0 of 3 . 3 . 8 is covered by u s i n g Li. Content: Edited by Page iii Copyright page Page iv Preface Pages vii-viii Chapter 1 Matrices Pages 1-20 Chapter 2 Classical Matrices Pages 21-38 Chapter 3 Triangles and Banach Space Pages 39-49 Chapter 4 FK Spaces Pages 51-73 Chapter 5 Replaceability and Consistency Pages 75-88 Chapter 6 Bigness Theorems Pages 89-102 Chapter 7 Sequence Spaces Pages 103-113 Chapter 8 Inclusion and Mapping Pages 115-140 Chapter 9 Semiconservative Spaces and Matrices Pages 141-156 Chapter 10 Distinguished Subspaces of FK Spaces Pages 157-178 Chapter 11 Extension Pages 179-186 Chapter 12 Distinguished Subspaces of Matrix Domains Pages 187-199 Chapter 13 Distinguished Subspaces of c A Pages 201-220 Chapter 14 The Functional μ Pages 221-232 Chapter 15 The Subspace P Pages 233-250 Chapter 16 Sequential Completeness and Separability Pages 251-261 Chapter 17 Maps of Banach Spaces Pages 263-279 Chapter 18 Algebra Pages 281-290 Chapter 19 Miscellany Pages 291-301 Bibliography Pages 303-308 Index Pages 309-318 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.

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 's'shard'' (classical) proofs are omitted; the theorems given all have 's'ssoft'' (functional analytic) proofs