## 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 1930

If & is 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 , then a

spectral measure E on E is called a resolution of the

If & is 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 , then a

spectral measure E on E is called a resolution of the

**identity**( or a spectral ...Page 2094

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X

is a weakly complete B - space , then any prespectral operator is automatically

spectral , and so has a unique resolution of the

] ...

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X

is a weakly complete B - space , then any prespectral operator is automatically

spectral , and so has a unique resolution of the

**identity**. Berkson and Dowson [ 1] ...

Page 2242

The projection valued measure E is said to be the resolution of the

13 LEMMA . An unbounded spectral operator of scalar type in the sense of

Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the ...

The projection valued measure E is said to be the resolution of the

**identity**for T.13 LEMMA . An unbounded spectral operator of scalar type in the sense of

Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the ...

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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