## Linear Operators: General theory |

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Page 68

The space X is said to be weakly complete if every weak Cauchy sequence has a weak

The space X is said to be weakly complete if every weak Cauchy sequence has a weak

**limit**. In Chapter V , a topology is introduced in certain linear spaces in such a way that they become Hausdorff spaces in which the notion of ...Page 126

We define the

We define the

**limit**inferior and the**limit**superior of { En } by the equations or lim inf En un Em , lim sup En nu Em m . 72 n = 1 men n n = 1 man If lim inf , ER = lim sup , Em , { En } is said to be convergent , and we write the ...Page 293

The

The

**limit**lim.n- Sein ( 8 ) u ( ds ) then exists for each E € and Corollary III.7.4 is contradicted . Conversely , suppose that K is bounded and that the integrals Set ( s ) u ( ds ) are countably additive uniformly with respect to f in ...### 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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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero