## 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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Doklady

5169 , 961 ( 1965 ) . 2 . On scattering operators and contraction semi - groups in

Hilbert space . Doklady

.

Doklady

**Akad**. Nauk SSSR 160 , 9–12 ( 1965 ) . ( Russian ) Math . Rev. 30 , #5169 , 961 ( 1965 ) . 2 . On scattering operators and contraction semi - groups in

Hilbert space . Doklady

**Akad**. Nauk SSSR 165 , 9–12 ( 1965 ) . ( Russian ) Math.

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Criteria for one - sided reversibility of elements of normed rings and their

applications . Doklady

Math . Rev. 27 # 6147 , 1175 ( 1964 ) . 6 . The factorization problem for operator

functions .

Criteria for one - sided reversibility of elements of normed rings and their

applications . Doklady

**Akad**. Nauk SSSR 145 , 971–974 ( 1962 ) . ( Russian )Math . Rev. 27 # 6147 , 1175 ( 1964 ) . 6 . The factorization problem for operator

functions .

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On the minimax principle for K - positive operators . Comment . Math . Univ .

Carolinae 7 , 109–112 ( 1966 ) . Markus , A. S. ( see also Gohberg , I. C. ) 1. The

root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

On the minimax principle for K - positive operators . Comment . Math . Univ .

Carolinae 7 , 109–112 ( 1966 ) . Markus , A. S. ( see also Gohberg , I. C. ) 1. The

root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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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