## 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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Results 1-3 of 71

Page 2005

By Theorem 6.4 the spectral operators with non - zero radical parts are the only

ones not

scalar type operators , and for any a and b in A , they are

operators .

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 ) arescalar type operators , and for any a and b in A , they are

**similar**to normaloperators .

Page 2400

Friedrichs ' Method of

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 , and even

much ...

Friedrichs ' Method of

**Similar**Operators In the present section we shall begin ourdiscussion 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 , and even

much ...

Page 2401

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

bounded operator U in Y with a bounded inverse such that S = U - 1TU . Note that

Definition 2 applies to unbounded operators as well as to bounded operators .

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

**similar**if there exists abounded operator U in Y with a bounded inverse such that S = U - 1TU . Note that

Definition 2 applies to unbounded operators as well as to bounded operators .

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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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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