## Linear Operators: General theory |

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Page 376

Weakly Compact Sets 13.13 13.14 6.29 6.29 6.14 Weak Cauchy Sequences

13.13 13.14 13.43 13.43 13.40 Weak Convergence to x 6.4 , 6.12 , 6.31 13.13

13.14 6.31 6.31 Y Convergence in X = y * meaningless

less ...

Weakly Compact Sets 13.13 13.14 6.29 6.29 6.14 Weak Cauchy Sequences

13.13 13.14 13.43 13.43 13.40 Weak Convergence to x 6.4 , 6.12 , 6.31 13.13

13.14 6.31 6.31 Y Convergence in X = y * meaningless

**meaning**less**meaning**.less ...

Page 534

L. ( S , E , u ) has a known

how to define L ( S , E , u ) . For 1 Spoo , L , is a B - space , but for 0 < p < 1 , L , is

merely an F - space ( cf. Exercise III.9.30 , where , however , the symbol , has a ...

L. ( S , E , u ) has a known

**meaning**; in the course of this section we will also seehow to define L ( S , E , u ) . For 1 Spoo , L , is a B - space , but for 0 < p < 1 , L , is

merely an F - space ( cf. Exercise III.9.30 , where , however , the symbol , has a ...

Page 684

Thus in - 1 1 n - 1 SE2 flqms ) u ( ds ) = Eu ( g - me ) Sn n m = 0 In order to be

able to assign a

conversely if ( 2 ) holds then the set function m in the proof of the preceding

theorem ...

Thus in - 1 1 n - 1 SE2 flqms ) u ( ds ) = Eu ( g - me ) Sn n m = 0 In order to be

able to assign a

**meaning**to. m = 0 g < Ki = Ku ( e ) , which proves ( 2 ) . Nowconversely if ( 2 ) holds then the set function m in the proof of the preceding

theorem ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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