## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 66

Page 464

( 3 ) For every fel ' , supzek Rf ( x ) < 0 ; moreover , each linear functional 0 on I

which

( 1 ) = f ( xo ) , for some x , € K. ( 4 ) I / KG , É < 0,0 a limit ordinal , is a monotone ...

( 3 ) For every fel ' , supzek Rf ( x ) < 0 ; moreover , each linear functional 0 on I

which

**satisfies**60 60 inf Rf ( x ) < RØ ( ) sup Rf ( x ) , fet ZEK TEK fel also**satisfies**( 1 ) = f ( xo ) , for some x , € K. ( 4 ) I / KG , É < 0,0 a limit ordinal , is a monotone ...

Page 495

We now prove that B , is an algebra under the natural product ( tg ) ( s ) = f ( s ) g (

s ) , se S. To see this , let h be a fixed element of C ( S ) and let B ( h ) = { f € Bolth

€ B. ) . Evidently B ( h ) C B. , and it is clear that B ( h )

We now prove that B , is an algebra under the natural product ( tg ) ( s ) = f ( s ) g (

s ) , se S. To see this , let h be a fixed element of C ( S ) and let B ( h ) = { f € Bolth

€ B. ) . Evidently B ( h ) C B. , and it is clear that B ( h )

**satisfies**properties ...Page 557

Consequently , the product R , of all the factors ( 1-7 ; ) * i in R such that a ; E O ( T

) , still

) Bi , where Bi min ( ais v ( 2 ; ) ) ,

Consequently , the product R , of all the factors ( 1-7 ; ) * i in R such that a ; E O ( T

) , still

**satisfies**R ( T ) = 0. In the same way , the product R , of all the factors ( 1-2 ;) Bi , where Bi min ( ais v ( 2 ; ) ) ,

**satisfies**R , ( T ) = 0. Since any polynomial P ...### 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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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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 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 transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero