## 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 2017

and the fraction in the

and the fraction in the

**inequality**( i ) of Theorem 6 is Isi - sl2 + 2 | 818212 { ( si - $ 2 ) * + 1681 $ * } 1/2 which is bounded on all of R " . Thus As has a resolution of the identity . Furthermore , the set S , is the null set { 8 ...Page 2190

Thus for some constant K we have | S ( f ) | SK \ f | and to prove the final

Thus for some constant K we have | S ( f ) | SK \ f | and to prove the final

**inequality**of the present theorem it will suffice to prove that lifle = S ( f ) . Since both terms in this**inequality**are ...Page 2399

By ( 44 ) and Hölder's

By ( 44 ) and Hölder's

**inequality**we have ( 45 ) { 1 * 10 * \ ve ) — ( $ * $ \ ( ) ? du din " " skal v 4. ) 29/1 Isla . The**inequality**( 42a ) follows immediately from ( 43 ) and ( 45 ) . Since the**inequality**( 42b ) may be deduced in a ...### 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 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