## 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 2005

4 the spectral operators with non - zero radical parts are the only ones not

to normal operators . Thus both of the operators in ( 57 ) are scalar type operators

, and for any a and b in A , they are

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 normal operators . In the case of ...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 2447

Applying the special case of Theorem 23 , which has already been proved , to the

mapping ( 1 / c ) + - 1GT , we find that ( 1 / c ) - 1G7 is

Applying the special case of Theorem 23 , which has already been proved , to the

mapping ( 1 / c ) + - 1GT , we find that ( 1 / c ) - 1G7 is

**similar**to J , so that G is**similar**to cJ . Q . E . D . 3 . The Friedrichs ' Method for the Discrete Spectrum XX .### 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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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 function 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