Bases in Banach spaces, Issue 1

Front Cover
Springer-Verlag - Banach spaces
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Contents

The Basis Problem Some Properties of Bases in Banach Spaces 1 Definition of a basis in a Banach space The basis problem Relations between bases i...
1
Some examples of bases_ in concrete Banach spaces Some separable
2
Banach spaces in which no basis is known
10
The coefficient functionals associated to a basis Bounded bases Nor malized bases
17
Biorthogonal systems The partial sum operators Some characteriza tions of regular biorthogonal systems Applications
23
Some characterizations of regular complete biorthogonal systems Multipliers
31
Some types of linear independence of sequences
50
Intrinsic characterizations of bases The norm and the index of a se quence The index of a Banach space Extension of block basic sequences
57
Classes of Bases not Involving Unconditional Convergence 1 Monotone and strictly monotone bases
214
Normal bases
252
Positive bases
261
4 shrinking bases
267
Bases of types ++ al+ and a+ The cone associated to a basis
315
11 Besselian and Hilbertian bases Stability theorems
337
12 Relations between various types of bases
359
Universal bases Complementably universal bases Blockuniversal
373

Domination and equivalence of sequences Equivalent affinely equiv alent and permutatively equivalent bases
68
Stability theorems of PaleyWiener type
84
Other stability theorems
93
11 An application to the basis problem
109
bases and sequence spaces
112
Bases in topological linear spaces Weak bases and bounded weak bases in Banach spaces Weak bases and bounded weak bases in conjugate Banach s...
144
Schauder bases in topological linear spaces Properties of weak duality for bases in Banach spaces
151
eSchauder bases and ASchauder bases in topological linear spaces
158
Some remarks on bases in normed linear spaces
160
Continuous linear operators in Banach spaces with bases
162
18 Bases of tensor products
171
19 Best approximation in Banach spaces with bases
174
Polynomial bases Strict polynomial bases T systems and A systems
187
Notes and remarks
200
Special Classes of Bases in Banach Spaces
213
Unconditional Bases and Some Classes of Unconditional Bases
396
15 Some separable Banach spaces having no unconditional basis
432
Some characterizations of unconditional bases among incomplete
458
Intrinsic characterizations of unconditional bases Some more separable
499
Equivalence and permutative equivalence of unconditional bases Uni
529
Best approximation in Banach spaces with unconditional bases
550
21 Subsymmetric bases
563
22 Symmetric bases Symmetric spaces
574
Existence of nonequivalent normalized bases and condi
602
Banach spaces with
609
Absolutely convergent bases Uniform bases
621
Bibliography
646
Notation Index
659
Subject Index
665
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