## Summability Through Functional AnalysisSummability 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

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 |

### Other editions - View all

### Common terms and phrases

Abel's identity absolutely convex Banach algebra Banach space Banach-Steinhaus theorem bounded divergent sequences bounded sequences bounded set Bx)n Cauchy closed subspace closure condition conservative matrix conull conull matrix convergent columns coregular matrix coregular triangle Corollary defined DEFINITION dense divergent sequence dual equipotent equivalent exists finite FK program FK space Frechet space functional analysis given growth sequence Hahn-Banach theorem Hausdorff hence implies includes inset integers invariant kth column Lemma Let Ax)n Let f limAx locally convex locally convex space matrix with convergent Mercerian monotone norm multiplicative Necessity notation of Remark null columns proof proved regular relative topology replaceable result follows row function row-finite seminorms shows Sufficiency summability suppose t(Ax tA)x Tauberian Theorem 12 Theorem 9 trivial u-continuous u-unique vector space weakly