## Linear Operators: Spectral operators |

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Page 2400

Friedrichs ' Method of

Friedrichs ' Method of

**Similar**Operators 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 2413

... exists a positive constant ε depending only on P , D , and c , such that the operators T and T + ( A ) are

... exists a positive constant ε depending only on P , D , and c , such that the operators T and T + ( A ) are

**similar**whenever || A || < € . Q.E.D. Theorem 1 and its corollaries are readily generalized to apply to unbounded operators .Page 2447

... to the mapping ( 1 / c ) ] , GJ , we find that ( 1/0 ) / - 1G ] is

... to the mapping ( 1 / c ) ] , GJ , we find that ( 1/0 ) / - 1G ] is

**similar**to J , so that G is**similar**to J. Q.E.D. 3. The Friedrichs ' Method for the Discrete Spectrum The XX.2.24 2447 FRIEDRICHS ' METHOD OF**SIMILAR**OPERATORS.### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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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