## Linear Operators: General theory |

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Page 81

general B - space by Hahn [ 2 ] who applied these results to a large number of ...

Banach and Steinhaus [ 1 ; p , 53 ] observed that in the case of a Bspace

**Theorems**1 . 11 , 1 . 17 , and 1 . 18 were proved for linear functionals on ageneral B - space by Hahn [ 2 ] who applied these results to a large number of ...

Banach and Steinhaus [ 1 ; p , 53 ] observed that in the case of a Bspace

**Theorem**1 .Page 729

, 8 ] , and F . Riesz [ 17 ] . Several generalizations of the mean ergodic

groups or semi - groups of operators more general than the discrete semi ...

**Theorems**for abstract vector lattices were proved by G . Birkhoff [ 2 ] , Kakutani [ 7, 8 ] , and F . Riesz [ 17 ] . Several generalizations of the mean ergodic

**theorem**togroups or semi - groups of operators more general than the discrete semi ...

Page 838

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela

883) Ascoli-Arzela

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela

**theorem**, on continuity of limit function, IV.6.11 (268) remarks concerning, (883) Ascoli-Arzela

**theorem**, on compactness of continuous functions, IV.6.7 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero