## Linear Operators: General theory |

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Page 464

( 3 ) For every f e T ' , sup.xek Rf ( x ) < 0o ; moreover , each linear functional Ø on l ' which

( 3 ) For every f e T ' , sup.xek Rf ( x ) < 0o ; moreover , each linear functional Ø on l ' which

**satisfies**inf Rf ( x ) < RÓ ( ) sup Rf ( x ) , fel → XeK ...Page 498

ΕΕΣ ΕεΣ Conversely , if æ * ( - ) on to X *

ΕΕΣ ΕεΣ Conversely , if æ * ( - ) on to X *

**satisfies**( i ) then ( ii ) defines an operator T on X to L ( S , E , u ) whose norm**satisfies**( iii ) .Page 557

Consequently , the product R , of all the factors ( 2–2 ; ) i in R such that hi e o ( T ) , still

Consequently , the product R , of all the factors ( 2–2 ; ) i in R such that hi e o ( T ) , still

**satisfies**R ( T ) = 0. In the same way , the product R ...### 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