## 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 2111

In order to handle quasi - nilpotent operators , Bishop introduces the notion of a

weak T - measure . He shows that an operator T in a

spectral operator if and only if each x ex has a weak T - measure and each * * e ...

In order to handle quasi - nilpotent operators , Bishop introduces the notion of a

weak T - measure . He shows that an operator T in a

**reflexive**B - space X is aspectral operator if and only if each x ex has a weak T - measure and each * * e ...

Page 2161

If ( iii ) is not true , then , since X is

theorem ( cf . Corollary II . 3 . 13 ) that there is an x in X with x * x # 0 and [ ( 101 *

– T * ) NX * ] x = 0 which means that ( 101 – T ) Nx = 0 . Since 2 * vanishes on the

...

If ( iii ) is not true , then , since X is

**reflexive**, it follows from the HahnBanachtheorem ( cf . Corollary II . 3 . 13 ) that there is an x in X with x * x # 0 and [ ( 101 *

– T * ) NX * ] x = 0 which means that ( 101 – T ) Nx = 0 . Since 2 * vanishes on the

...

Page 2176

However , when X is a

€ [ 0 , 27 ] a pair ( Er , Fe ) of closed subspaces which are invariant under T and

which resemble the manifolds corresponding to a resolution of the identity .

However , when X is a

**reflexive**B - space , Lorch was able to construct for each 0€ [ 0 , 27 ] a pair ( Er , Fe ) of closed subspaces which are invariant under T and

which resemble the manifolds corresponding to a resolution of the identity .

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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