## 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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Results 1-3 of 85

Page 1948

The sum and the product of two

space are also spectral operators . The proof of this corollary will use the

following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space

with A ...

The sum and the product of two

**commuting**bounded spectral operators in Hilbertspace are also spectral operators . The proof of this corollary will use the

following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space

with A ...

Page 2098

when N is a quasi - nilpotent which may not

imply that o ( T ) = 0 , ( T ) . ... ( T ) = [ 0 , 1 ] with a bounded

continuous family E ( t ) , te [ 0 , 1 ] , of projections such that ( i ) E ( 0 ) = 0 , E ( 1 )

= I , ( ii ) ...

when N is a quasi - nilpotent which may not

**commute**with T . The conditionsimply that o ( T ) = 0 , ( T ) . ... ( T ) = [ 0 , 1 ] with a bounded

**commuting**stronglycontinuous family E ( t ) , te [ 0 , 1 ] , of projections such that ( i ) E ( 0 ) = 0 , E ( 1 )

= I , ( ii ) ...

Page 2177

Introduction The sum and product of two

in Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen

that this principle could be extended to the sum and product of two

Introduction The sum and product of two

**commuting**bounded normal operatorsin Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen

that this principle could be extended to the sum and product of two

**commuting**...### 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