## Linear Operators: General theory |

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Page 462

**Banach**and Saks [ 1 ] proved that every weakly convergent sequence { x , } in L , ( 0 , 1 ) or lp , p > 1 , contains a subsequence { y : } which is ( C ...Page 804

Perturbations of linear operators in

Perturbations of linear operators in

**Banach**spaces . Arch . Math . 6 , 89–101 ( 1955 ) . Rosenthal , A. ( see Hahn , H. , and Hartogs , F. ) Rosser , J. B. ...Page 810

Weak compactness in

Weak compactness in

**Banach**spaces . Studia Math . 11 , 71-94 ( 1950 ) . Skorohod , A. ( see Kostyučenko , A. ) Slobodyanskii , M. G. 1.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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### Common terms and phrases

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