## 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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By Theorem 6.4 the spectral operators with non - zero radical parts are the only ones not

By Theorem 6.4 the spectral operators with non - zero radical parts are the only ones not

**similar**to normal operators . Thus both of the operators in ( 57 ) are scalar type operators , and for any a and b in A , they are**similar**to ...Page 2400

Friedrichs ' Method of

Friedrichs ' Method of

**Similar**Operators a In the present section we shall begin our discussion of an elegant method , due to K. 0. Friedrichs , which makes it possible to show , in a variety of cases , that an operator is spectral ...Page 2401

Two operators S and T in a B - space Y are called

Two operators S and T in a B - space Y are called

**similar**if there exists a bounded operator U in Y with a bounded inverse such that S = U - TU . Note that Definition 2 applies to unbounded operators as well as to bounded operators .### What people are saying - Write a review

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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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### 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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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