## Linear Operators: General theory |

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that is , for every a e A , the

that is , for every a e A , the

**function f**assigns an element f ( a ) € B. If | : A + B and g : B → C , then the mapping gf : A + C is defined by the ...Page 196

For each s in S , F ( s ) is an equivalence class of functions , any pair of whose ... If for each s we select a particular

For each s in S , F ( s ) is an equivalence class of functions , any pair of whose ... If for each s we select a particular

**function f**( s , • ) € F ( s ) ...Page 199

integral Ss / ( s , t ) u ( ds ) , as a

integral Ss / ( s , t ) u ( ds ) , as a

**function of**t , is equal to the element Ss F ( s ) u ( ds ) of L ( T , ET , 2 , X ) . Proof .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad 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 semi-group 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