## Linear Operators: General theory |

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that is , for every a € A , the

that is , for every a € A , the

**function f**assigns an element f ( a ) € B. If f : A + B and g : B → C , then the ... The set f ( C ) is called the image of C and the set f - 1 ( D ) is called the inverse image of D. Iff : A → A and ...Page 103

space of all functions which map S into X ( see 1.6.1 ) . Unfortunately , this is rarely the case and so a slight detour will be made . 3 DEFINITION . The

space of all functions which map S into X ( see 1.6.1 ) . Unfortunately , this is rarely the case and so a slight detour will be made . 3 DEFINITION . The

**function f**on S to X is said to be a u - null function or , when u is understood ...Page 196

Suppose that ( S , E , u ) is a measure space and

Suppose that ( S , E , u ) is a measure space and

**F**is a u - measurable**function**whose values are in L ( T , ET , 2 ) , 1 sp < 0. For each s in S ,**F**( s ) is an equivalence class**of functions**, any pair**of**whose members coincide a ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero