## 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 1953

First

First

**suppose**that = 0.If TX is not dense then , by Corollary II.3.13 , there is an x * in X * with x * # 0 and ** TX = 0 . Let x1 # 0 and define the operator A by the equation Ax = x * ( x ) x1 , so that A +0 .Page 2284

However , rather than seek the maximum generality , it will be convenient to

However , rather than seek the maximum generality , it will be convenient to

**suppose**that B is itself complete and satisfies the countable chain condition . Both these properties hold for B if X is separable , so this will be assumed ...Page 2303

**Suppose**that E is its resolution of the identity , and**suppose**that { n } is an enumeration of its spectrum . Let dn denote the distance from In to o ( T ) — { n } .**Suppose**that for all but a finite number of n , E ( An ) has a ...### 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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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