## 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 2152

To

x € X , ( x ) $ 8 } . It will be shown that M ( 8 ) is closed . For every x we have g ( x )

= o ( T ) sro and thus M ( S ) = M ( ST . ) , which allows us to assume , with no ...

To

**prove**( C ) , let & be a closed subset of the complex plane and let M ( 8 ) = { x |x € X , ( x ) $ 8 } . It will be shown that M ( 8 ) is closed . For every x we have g ( x )

= o ( T ) sro and thus M ( S ) = M ( ST . ) , which allows us to assume , with no ...

Page 2236

This

) + g ( T ) ) and let { en } be as above . Then , since T | E ( en ) X is bounded ,

statements ( i ) and ( ii ) and the functional calculus of bounded operators ( cf . VII

.

This

**proves**( iii ) . The proof of ( viii ) is evident . To**prove**( vi ) , let x be in D ( f ( T) + g ( T ) ) and let { en } be as above . Then , since T | E ( en ) X is bounded ,

statements ( i ) and ( ii ) and the functional calculus of bounded operators ( cf . VII

.

Page 2459

Xn = x , then , by what we have already

where yı € Lac ( H ) and Y2 , Yz are orthogonal to Eac ( H ) . But , since ... Using

this last fact , it is easy to

...

Xn = x , then , by what we have already

**proved**, we may write x = yı + y2 + Yu ,where yı € Lac ( H ) and Y2 , Yz are orthogonal to Eac ( H ) . But , since ... Using

this last fact , it is easy to

**prove**assertion ( c ) of the present lemma . We argue as...

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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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