Sequence spaces

Cover......Page 1
Title: Sequence spaces......Page 2
ISBN 0-273.-08507-7......Page 3
Preface......Page 4
Contents......Page 6
1. ORIENTATION, CLASSIFICATION OF TYPICAL PROBLEMS......Page 8
1.5 Assignment of topologies.......Page 9
2. EXAMPLES OF SEQUENCE SPACES......Page 10
Exercises......Page 12
3. ALGEBRAIC AND COMBINATORIAL PROPERTIES......Page 13
Exercises......Page 15
4. GALOIS DUALITY THEORY WITH RESPECT TO PRODUCT AND CONVOLUTION......Page 16
Exercises......Page 19
5. METHODS OF GENERATING SEQUENCE SPACES......Page 20
Exercises......Page 24
NOTES ON CHAPTER ONE......Page 25
1. INTRODUCTION......Page 27
Exercises......Page 34
2. THE NORMAL TOPOLOGY ON KOTHE SPACES......Page 36
3. SCHWARTZ AND NUCLEAR SEQUENCE SPACES......Page 41
Exercises......Page 49
4. MACKEY AND STRONG TOPOLOGIES......Page 51
Exercises......Page 57
5. REPRESENTATION OF FUNCTION SPACES......Page 58
1. A GENERALIZATION OF THE KOTHE-TOEPLITZ DUALITY THEORY......Page 64
2. THE ZELLER THEORY OF FK-SPACES......Page 66
Exercises......Page 71
3. phi-DUALITY THEORY......Page 72
Exercises......Page 75
4. COMPARISON OF THE GENERALIZED KOTHE-TOEPLITZ THEORY WITH THE phi-DUALITY THEORY. SUM SPACES......Page 76
5. LATTICES OF LOCALLY CONVEX K-SPACES......Page 82
Exercises......Page 89
6. FURTHER LATTICE PROPERTIES OF LOCALLY CONVEX K-SPACES......Page 90
7. ABELIAN AND TAUBERIAN THEOREMS......Page 94
Exercises......Page 101
NOTES ON CHAPTER THREE......Page 102
1. MATRIX MAPPINGS BETWEEN CERTAIN SPACES, CONTINUITY......Page 103
2. THE PREIMAGE OF A MATRIX, ZK-SPAC......Page 108
The Theorems of Silverman-Toeplitz and Kojma-Schur......Page 111
3.3 Theorem (Silverman-Toeplitz......Page 112
Exercise......Page 114
4. MAPPINGS FROM L^1, bvo , bv; THE THEOREM OF LORENTZ AND KNOPP......Page 117
5. MATRIX MAPPINGS FROM l^2 INTO l^2......Page 118
6. DIAGONALS OF MATRIX MAPPINGS......Page 123
7. THE MULTIPLIER ALGEBRA OF A SEQUENCE SPACE......Page 129
8. THE MULTIPLIER ALGEBRA m......Page 140
9. MAPPINGS FROM l^P INTO l^q (p > q): A THEOREM OF PITT......Page 145
Exercises......Page 147
10. THE SHIFT OPERATOR AND CONVOLUTION......Page 148
11. SOME RESULTS ON (S -* T) AND M* (S), AN APPLICATION TO DIFFERENCE EQUATIONS......Page 151
Exercises......Page 156
12. MATRIX MAPPINGS OF KOTHE SPACES......Page 157
NOTES ON CHAPTER FOUR......Page 164
1. SOME PROBLEMS OF SUMMABILITY THEORY......Page 166
2. NORLUND AND CESARO MEANS......Page 168
3. HAUSDORFF MEANS......Page 174
Exercises......Page 180
4. TOPOLOGICAL PROPERTIES OF cA......Page 181
5. THE EXTENT OF cA......Page 186
Exercises......Page 196
6. THE BOUNDED CONSISTENCY THEOREM......Page 197
NOTES ON CHAPTER 5......Page 201
References......Page 202