## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2263

Under the hypotheses of the preceding theorem , every point de o , with the sole

possible exception of the point vo ,

spectral operator S. The point ve

spectrum ...

Under the hypotheses of the preceding theorem , every point de o , with the sole

possible exception of the point vo ,

**belongs**to the continuous spectrum of thespectral operator S. The point ve

**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 ( { 2 } ) = 0 for a #vo , deo ; thus , each such , 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 ( { 2 } ) = 0 for a #vo , deo ; thus , each such , must

**belong**to the continuous...

Page 2462

Moreover , if C

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 > there exists a finite set ...

Moreover , if C

**belongs**to the trace class 61 , then TnC converges to zero in tracenorm , 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 > there exists a finite set ...

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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