## 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 2263

Under the hypotheses of the preceding theorem , every point deo , with the sole possible exception of the point vo ,

Under the hypotheses of the preceding theorem , every point deo , with the sole possible exception of the point vo ,

**belongs**to the continuous spectrum of the spectral operator S. The point ve**belongs**to the point or to the continuous ...Page 2264

then ,

then ,

**belongs**neither to the point nor to the residual spectrum of S. Using the formula for the spectral resolution of S given by the preceding theorem , we find that E ( { 2 } ) = 0 for # vo , deo ; thus , each such a must**belong**to ...Page 2462

Moreover , if C

Moreover , if C

**belongs**to the trace class C1 , then T , C converges to zero in trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( { xe H || 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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