## 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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Page 1934

Since , by VII.3.4 , lim x * x ( ) = lim x * R ( E ; T ' ) . x = 0 , $ x $ > $ → it is

Since , by VII.3.4 , lim x * x ( ) = lim x * R ( E ; T ' ) . x = 0 , $ x $ > $ → it is

**seen**that x * x ( $ ) = 0 for all & and all x * e X * . Hence , by Corollary II.3.14 , x ( 8 ) = 0 and thus x = ( $ I - T ' ) 3 ( E ) = 0 .Page 2163

It is

It is

**seen**from Corollary XV.3.7 that F ( $ ) also commutes with the projections in the range of E , that is , ( iii ) F ( $ ) E ( 0 ) = E ( 0 ) F ...Page 2183

On the other hand , since PB contains all the elements of A ( B ) which have the form ( ii ) , and since this set of elements is dense in A ( B ) , it will be

On the other hand , since PB contains all the elements of A ( B ) which have the form ( ii ) , and since this set of elements is dense in A ( B ) , it will be

**seen**that PA ( T ) = A ( B ) . Moreover , it is clear that ( I – P ) B = R ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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