## 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

The relation of being quasi - nilpotent

The relation of being quasi - nilpotent

**equivalent**is indeed an equivalence relation and , when T and U are quasi - nilpotent**equivalent**, then ( i ) o ( T ) = g ( U ) , ( ii ) T has the single valued extension property if and only if U ...Page 2105

Berkson [ 2 ] showed that if E is a bounded spectral measure and if one defines || 2 || = sup { var x * E ( - ) w || * = 1 } , then I. || is a norm

Berkson [ 2 ] showed that if E is a bounded spectral measure and if one defines || 2 || = sup { var x * E ( - ) w || * = 1 } , then I. || is a norm

**equivalent**to | : | and relative to which all the operators E ( 8 ) become Hermitian .Page 2115

It is proved that if T is decomposable and 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 ) = Xu ( F ) for all closed sets F if and only if T and U are quasi ...### What people are saying - Write a review

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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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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero