## 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 54

Page 1930

If Eis a Boolean algebra of subsets of the complex plane which contains the void

set and the whole plane , in short , if & is a

a spectral measure E on & is called a resolution of the identity ( or a spectral ...

If Eis a Boolean algebra of subsets of the complex plane which contains the void

set and the whole plane , in short , if & is a

**field**of sets in the complex plane , thena spectral measure E on & is called a resolution of the identity ( or a spectral ...

Page 2143

Let T be a bounded linear operator in the complex B - space X . Then there is a

unique spectral measure on the

( T ) , g ( x ) Ş8 , de S ( T ) , ( 2 ) 58 ' . This spectral measure is bounded , is ...

Let T be a bounded linear operator in the complex B - space X . Then there is a

unique spectral measure on the

**field**S ( T ) with the properties E ( S ) x = x , de S( T ) , g ( x ) Ş8 , de S ( T ) , ( 2 ) 58 ' . This spectral measure is bounded , is ...

Page 2145

Second , the

first of these difficulties will be eliminated by the hypothesis ( C ) , to be made

presently . The second of these difficulties leads us to consider operators which

are ...

Second , the

**field**S ( T ) or the o -**field**M ( T ) may not contain all Borel sets . Thefirst of these difficulties will be eliminated by the hypothesis ( C ) , to be made

presently . The second of these difficulties leads us to consider operators which

are ...

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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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### 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 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