## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Results 1-3 of 91

Page 1934

PROOF . Using Theorem 2 , we see that if g ( x ) is void , then x ( ) is everywhere

defined , single valued , and hence entire . Since , by VII . 3 . 4 , lim x * x ( ) = lim x

* R ( É ; T ' ) . x = 0 , $ 200 $ 700 it is

PROOF . Using Theorem 2 , we see that if g ( x ) is void , then x ( ) is everywhere

defined , single valued , and hence entire . Since , by VII . 3 . 4 , lim x * x ( ) = lim x

* R ( É ; T ' ) . x = 0 , $ 200 $ 700 it is

**seen**that x * x ( $ ) = 0 for all & and all x * e ...Page 2163

8 , it is

( 6 . ) – F ( E ) B ( 0 , 05 ) SK sup | F ( Xi ) – F ( 81 ) , where the supremum is taken

over those i and j for which o ; o ; is not void . If by the norm ( 7 | is understood ...

8 , it is

**seen**that , for some constant K , 3 F46 . JE ( 0 . ) – É PLE ) E ( 0 ) | FIĚ Ž { P( 6 . ) – F ( E ) B ( 0 , 05 ) SK sup | F ( Xi ) – F ( 81 ) , where the supremum is taken

over those i and j for which o ; o ; is not void . If by the norm ( 7 | is understood ...

Page 2185

Since every function f in C ( 1 ) is bounded and Borel measurable , the integral s f

( a ) A ( dà ) exists and it is

now be shown that A is a spectral measure in X * . By placing f = 1 in ( ii ) , it is ...

Since every function f in C ( 1 ) is bounded and Borel measurable , the integral s f

( a ) A ( dà ) exists and it is

**seen**from ( i ) that ( ii ) S * ( 4 ( da ) , feC ( 1 ) . It willnow be shown that A is a spectral measure in X * . By placing f = 1 in ( ii ) , it is ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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