## 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 2056

This principle does not contradict Gödel's Theorem but does presuppose the

exclusion of selfcontradictory

a sick man would suffer from the

This principle does not contradict Gödel's Theorem but does presuppose the

exclusion of selfcontradictory

**statements**, the ... such unfortunate disturbances asa sick man would suffer from the

**statement**“ I shall not recover from this disease .Page 2236

Then , since T | E ( en ) X is bounded ,

calculus of bounded operators ( cf. ... In the first case described in

o ( T ) is a compact subset of U , and by Corollary XV.3.5 , E ( o ( T ) ) = 1 so that ...

Then , since T | E ( en ) X is bounded ,

**statements**( i ) and ( ii ) and the functionalcalculus of bounded operators ( cf. ... In the first case described in

**statement**( v ) ,o ( T ) is a compact subset of U , and by Corollary XV.3.5 , E ( o ( T ) ) = 1 so that ...

Page 2239

T ( fxə ) E ( e ) X = T ( fxě ) x , so that Qo is well defined on Ueeso E ( e ) X . It thus

follows from Lemma 6 that T ( f ) is a closed , densely defined operator . Moreover

,

T ( fxə ) E ( e ) X = T ( fxě ) x , so that Qo is well defined on Ueeso E ( e ) X . It thus

follows from Lemma 6 that T ( f ) is a closed , densely defined operator . Moreover

,

**statement**( g ) follows from Corollary 7 .**Statement**( d ) is obvious . Letting e e ...### 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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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