## 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 1964

Thus the triple ( S , E , e ) constitutes what we shall call a complete and countably additive self adjoint

Thus the triple ( S , E , e ) constitutes what we shall call a complete and countably additive self adjoint

**measure space**of projections in H. Associated with the spectral**measure space**( S , E , e ) is the B * -algebra eB ( S , 2 ) of ...Page 1983

Let A be in AP and let S be a compact space . ... E , ds ) where & is the o - field of Lebesgue measurable sets and ds is Lebesgue measure . ... that the

Let A be in AP and let S be a compact space . ... E , ds ) where & is the o - field of Lebesgue measurable sets and ds is Lebesgue measure . ... that the

**measure spaces**( RN , E , ds ) and ( S , E , ās ) are the same .Page 2110

One of the most surprising results due to Walsh [ 2 ] is the result that if M is an equicontinuous Borel spectral

One of the most surprising results due to Walsh [ 2 ] is the result that if M is an equicontinuous Borel spectral

**measure**into the**space**of continuous operators in a**space**E in which closed bounded sets are compact ( for example ...### What people are saying - Write a review

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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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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 defined Definition denote dense determined differential operator discrete 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