## 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 2092

I ] the following idea is introduced : Let T , U = B ( x ) and let ( T - USB = = ( - 1 ) ^ -

^ ( T + U - 1 ; CO then we say that T and U are quasi - nilpotent

lim ( T – U ) [ n ] | 1 / n = lim | ( U – T ) [ n ] | 11n = 0 . n + 11 + ( It is clear that if U ...

I ] the following idea is introduced : Let T , U = B ( x ) and let ( T - USB = = ( - 1 ) ^ -

^ ( T + U - 1 ; CO then we say that T and U are quasi - nilpotent

**equivalent**in caselim ( T – U ) [ n ] | 1 / n = lim | ( U – T ) [ n ] | 11n = 0 . n + 11 + ( It is clear that if U ...

Page 2105

Berkson ( 2 ) showed that if E is a bounded spectral measure and if one defines |

| 3 | | = sup { var æ * E ( - ) w | 12 * 1 = 1 } , then | | · | | is a norm

and relative to which all the operators E ( 8 ) become Hermitian . It follows from ...

Berkson ( 2 ) showed that if E is a bounded spectral measure and if one defines |

| 3 | | = sup { var æ * E ( - ) w | 12 * 1 = 1 } , then | | · | | is a norm

**equivalent**to 1 : 1and relative to which all the operators E ( 8 ) become Hermitian . It follows from ...

Page 2115

It is proved that if T is decomposable and T and U are quasi - nilpotent

, then U is decomposable . Moreover , if T and U are decomposable , then X ( F )

= xy ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...

It is proved that if T is decomposable and T and U are quasi - nilpotent

**equivalent**, then U is decomposable . Moreover , if T and U are decomposable , then X ( F )

= xy ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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