## 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 ( gf ) ( a ) = g ( /

( a ) ) for a € A . If f : A + B and CCA , the symbol / ( 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 ( gf ) ( a ) = g ( /

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

Page 104

It is customary to speak of the elements

functions rather than sets of equivalent ... Thus a function y can not be considered

as defined on the space F ( S , E , M , X ) , unless y ( t ) = y ( g ) whenever | - g is a

null ...

It is customary to speak of the elements

**of F**( S , E , H , X ) as if they werefunctions rather than sets of equivalent ... Thus a function y can not be considered

as defined on the space F ( S , E , M , X ) , unless y ( t ) = y ( g ) whenever | - g is a

null ...

Page 196

Next we study the relation between the theory

theory

and

Next we study the relation between the theory

**of**product measures and thetheory

**of**vector valued integrals . ... Suppose that ( S , E , u ) is a measure spaceand

**F**is a u - measurable**function**whose values are in L ( T , ET , 2 ) , 13p < 0.### What people are saying - Write a review

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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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### Common terms and phrases

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