## 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 1913

In Chapter XV we try to stress most of the basic elementary

In Chapter XV we try to stress most of the basic elementary

**properties**of spectral operators that distinguish them from other operators . These**properties**assume a variety of forms not immediately apparent from the definition of a ...Page 2134

Statement of the Problem In the preceding chapter we studied the

Statement of the Problem In the preceding chapter we studied the

**properties**of bounded spectral operators , that is , operators which have a countably additive resolution of the identity defined on the field of Borel sets .Page 2588

XVII.3.1 ( 2195 ) existence of multiplicity function for , XVIII.3.8 ( 2267 ) multiplicity function for , XVIII.3.1 ( 2264 ) , XVIII.3.3 ( 2265 )

XVII.3.1 ( 2195 ) existence of multiplicity function for , XVIII.3.8 ( 2267 ) multiplicity function for , XVIII.3.1 ( 2264 ) , XVIII.3.3 ( 2265 )

**properties**of , XVII.3.3 ( 2196 ) , XVII.3.4 ( 2197 ) , XVII.3.5 ( 2198 ) , XVII.3.6 ...### 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