## 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 2291

A number of results concerning the conditional convergence of eigenvalue

expansions are mentioned in Section 6 below . 2 . The Principal Abstract

whose ...

A number of results concerning the conditional convergence of eigenvalue

expansions are mentioned in Section 6 below . 2 . The Principal Abstract

**Perturbation**Theorem In this section we shall study**perturbations**of an operatorwhose ...

Page 2530

Amer . Math . Soc . , Providence , R . I . , 1965 . 18 . Spectral

phenomena .

Wiley , New ...

**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 ,Wiley , New ...

Page 2546

Soc . Japan 11 , 246 – 262 ( 1959 ) . II . ibid . 12 , 243 – 257 ( 1960 ) . 4 . On a

generalization of the Weinstein - Aronszajn formula and the infinite determinant .

Sci .

**Perturbation**of continuous spectra by unbounded operators , I , II . I . J . Math .Soc . Japan 11 , 246 – 262 ( 1959 ) . II . ibid . 12 , 243 – 257 ( 1960 ) . 4 . On a

generalization of the Weinstein - Aronszajn formula and the infinite determinant .

Sci .

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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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### Common terms and phrases

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