## Linear Operators: Spectral operators |

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Page 2094

Berkson and Dowson [ 1 ] have considered prespectral operators in some detail

and have obtained a number of results concerning them . They show that if T is

spectral , then 7 * has a unique resolution of the identity of class ( X ) ;

if ...

Berkson and Dowson [ 1 ] have considered prespectral operators in some detail

and have obtained a number of results concerning them . They show that if T is

spectral , then 7 * has a unique resolution of the identity of class ( X ) ;

**moreover**,if ...

Page 2115

F if and only if T and U are quasi - nilpotent equivalent . If T is a spectral operator

and T and U are quasi - nilpotent equivalent , then U is a spectral operator .

**Moreover**, if T and U are decomposable , then X1 ( F ) = xy ( F ) for all closed setsF if and only if T and U are quasi - nilpotent equivalent . If T is a spectral operator

and T and U are quasi - nilpotent equivalent , then U is a spectral operator .

Page 2356

Then by Definition XVIII . 2 . 8 , a vector x in E ( oo ) X is in D ( $ ( T ) ) if and only if

it is in D ( F ( S ) ) , and ,

defined on o ( T ) and for x e E ( 0 . ) X . In particular , x is in D ( T ' ) if and only if x

...

Then by Definition XVIII . 2 . 8 , a vector x in E ( oo ) X is in D ( $ ( T ) ) if and only if

it is in D ( F ( S ) ) , and ,

**moreover**f ( T ) x = f ( S ) x , for each analytic function fdefined on o ( T ) and for x e E ( 0 . ) X . In particular , x is in D ( T ' ) if and only if x

...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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