## 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 ,

spectral operator S . The point vo

spectrum ...

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 thespectral operator S . The point vo

**belongs**to the point or to the continuousspectrum ...

Page 2264

then

formula for the spectral resolution of S given by the preceding theorem , we find

that E ( { a } ) = 0 for a # vordeo ; thus , each such a must

...

then

**belongs**neither to the point nor to the residual spectrum of S . Using theformula for the spectral resolution of S given by the preceding theorem , we find

that E ( { a } ) = 0 for a # vordeo ; thus , each such a must

**belong**to the continuous...

Page 2462

Moreover , if C

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 exists a

finite ...

Moreover , if C

**belongs**to the trace class C1 , then TnC converges to zero intrace 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 exists a

finite ...

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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