## Linear Operators: Spectral operators |

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The Principal Abstract

The Principal Abstract

**Perturbation**Theorem In this section we shall study**perturbations**of an operator whose resolvent is compact . The principal result gives conditions under which such an operator ...Page 2510

Various of the

Various of the

**perturbation**- theoretic ideas touched on explicitly or by indirection in the present chapter are developed systematically by T. Kato in his treatise [ 13 ] . This treatise also contains an extensive bibliography of ...Page 2530

**Perturbation**of spectra in Hilbert space . Lectures in Applied Math . , Vol . III , Amer . Math . Soc . , Providence , R. I. , 1965 . 18. Spectral**perturbation**phenomena .**Perturbation**Theory and its Applications in Quantum Mechanics ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator Amer analytic applications arbitrary assume B-space Banach space belongs Boolean algebra Borel sets 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 example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity Nauk norm normal perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero