## 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 XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero