## Linear Operators: General theory |

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Page 3

that is , for every a € A , the

g : B → C , then the mapping gf : A → C is defined by the equation ( g / ) ( a ) = g (

/ ( a ) ) for a € A. If f : A → B and C ÇA , the symbol f ( C ) is used for the set of all ...

that is , for every a € A , the

**function f**assigns an element f ( a ) € B. If f : A + B andg : B → C , then the mapping gf : A → C is defined by the equation ( g / ) ( a ) = g (

/ ( a ) ) for a € A. If f : A → B and C ÇA , the symbol f ( C ) is used for the set of all ...

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

on S to X is said to be a u - null function or , when u is understood , simply a null ...

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 , simply a null ...

Page 196

For each s in S , F ( s ) is an equivalence class of functions , any pair of whose

members coincide a - almost everywhere . 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

members coincide a - almost everywhere . If for each s we select a particular

**function f**( s , . ) € F ( s ) , the resulting**function f**( s , t ) defined on ( R , ER ...### 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