## Bases in Banach spaces, Issue 1 |

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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 |

Copyright | |