## Linear Operators: Spectral operators |

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Page 2152

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. To

C ) , let & be a closed subset of the complex plane and let M ( S ) = { w X e X , 0 (

x ) 58 } . It will be shown that M ( S ) is closed . For every x we have o ( x ) 5 o ( T )

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. To

**prove**(C ) , let & be a closed subset of the complex plane and let M ( S ) = { w X e X , 0 (

x ) 58 } . It will be shown that M ( S ) is closed . For every x we have o ( x ) 5 o ( T )

...

Page 2236

To

since T | Elen ) X is bounded , statements ( i ) and ( ü ) and the functional calculus

of bounded operators ( cf . VII . 3 . 10 ) may be applied to conclude that lim ( f + 9 )

...

To

**prove**( vi ) , let x be in D ( $ ( T ) + g ( T ) ) and let { en } be as above . Then ,since T | Elen ) X is bounded , statements ( i ) and ( ü ) and the functional calculus

of bounded operators ( cf . VII . 3 . 10 ) may be applied to conclude that lim ( f + 9 )

...

Page 2459

Xin = x , then , by what we have already

where y , e Lac ( H ) and Y2 , Yz are orthogonal to ac ( H ) . But , since ... Using

this last fact , it is easy to

...

Xin = x , then , by what we have already

**proved**, we may write x = yı + y2 + Ys ,where y , e Lac ( H ) and Y2 , Yz are orthogonal to ac ( 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 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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