## Linear Operators: General theory |

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Page 464

( 3 ) For every f e l ' , supwek Rf ( x ) < 00 ; moreover , each linear functional Ø on l ' which

( 3 ) For every f e l ' , supwek Rf ( x ) < 00 ; moreover , each linear functional Ø on l ' which

**satisfies**inf Rf ( x ) < RO ( 1 ) S sup Rf ( x ) , fel XEK TEK also**satisfies**Φ ( ; ) ) = f ( xo ) , fel for some X , € K. ( 4 ) If KĘ ...Page 498

ΕΕΣ ΕΕΣ Conversely , if x * ( ) on to X *

ΕΕΣ ΕΕΣ Conversely , if x * ( ) on to X *

**satisfies**( i ) then ( ii ) defines an operator T on X to L ( S , E , u ) whose norm**satisfies**( iii ) . Furthermore T is weakly compact if and only if x * ( ) is countably additive on in the ...Page 557

Consequently , the product R , of all the factors ( 1-2 ; ) * in R such that i ; E O ( T ) , still

Consequently , the product R , of all the factors ( 1-2 ; ) * in R such that i ; E O ( T ) , still

**satisfies**R ( T ) = 0. In the same way , the product R , of all the factors ( 2--2 ; ) Bi , where Bi min ( ai , v ( ai ) ) ,**satisfies**R ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero