## 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 |

### From inside the book

Results 1-3 of 90

Page 1930

The operators we shall study in the next few chapters will be operators which

have a

identity which are countably additive on the field B of Borel sets in the plane .

The operators we shall study in the next few chapters will be operators which

have a

**resolution**of the identity with ... We shall , in fact , study**resolutions**of theidentity which are countably additive on the field B of Borel sets in the plane .

Page 2094

12 ) that if X is a weakly complete B - space , then any prespectral operator is

automatically spectral , and so has a unique

and Dowson [ 1 ] have considered prespectral operators in some detail and have

...

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 . Berksonand Dowson [ 1 ] have considered prespectral operators in some detail and have

...

Page 2242

The projection valued measure E is said to be 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 | |

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