## 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

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

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

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 .Page 2242

The projection valued measure E is said to be 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.### 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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### 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