## 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 2236

Then , since T | E ( en ) X is bounded ,

calculus of bounded operators ( cf . VII . 3 . ... In the first case described in

( T ) ...

Then , since T | E ( en ) X is bounded ,

**statements**( i ) and ( ii ) and the functionalcalculus of bounded operators ( cf . VII . 3 . ... In the first case described in

**statement**( v ) , o ( T ) is a compact subset of U , and by Corollary XV . 3 . 5 , E ( o( T ) ...

Page 2239

# 0 , and h ( s ) = 0 otherwise . Then sh ( s ) 5 1 , so that by ( c ) the operator T ...

**Statement**( a ) clearly will follow from**statement**( b ) .**Statement**( b ) follows from**statement**( f ) ; indeed , let | f ( s ) 2 \ g ( s ) ] , and puth ( s ) = g ( s ) / S ( 8 ) if f ( 8 )# 0 , and h ( s ) = 0 otherwise . Then sh ( s ) 5 1 , so that by ( c ) the operator T ...

Page 2476

We therefore see that , as asserted ,

that gi ( a ) = 0 for all a key . Since ( H + V , H ) is a closed subspace of H ' ( cf .

Lemma 2 ) it follows that every s e H ' such that gi ( a ) = 0 for all a € e , belongs to

...

We therefore see that , as asserted ,

**statement**( 76 ) holds for each se H ' suchthat gi ( a ) = 0 for all a key . Since ( H + V , H ) is a closed subspace of H ' ( cf .

Lemma 2 ) it follows that every s e H ' such that gi ( a ) = 0 for all a € e , belongs to

...

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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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