## 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 ) = 0 ( U ) , ( ii ) T has the single valued extension property if and only if U ...Page 2105

is a norm

is a norm

**equivalent**to 1 : 1 and relative to which all the operators E ( 8 ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then 11 56 ( 8 ) E ( ds ) || = sup ...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 XT ( 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 | |

28 other sections not shown

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### Common terms and phrases

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 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