## Linear Operators: General theory |

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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 f ( C ) is used for the set of all ...

that is , for every a € A , the

**function f**assigns an element f ( a ) € B . Iff : 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 f ( C ) is used for the set of all ...

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 C CA , 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 | : 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 C CA , the symbol f ( C ) is used for the set of all ...

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 ) , 15p < 0 .### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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