## Linear Operators: Spectral operators |

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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 2413

We may now apply Theorem 1 to conclude that there exists a positive constant ε

depending only on P , D , and c , such that the operators T and T + ( A ) are

We may now apply Theorem 1 to conclude that there 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 ...Page 2447

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

mapping ( 1 / c ) + - GJ , we find that ( 1 / c ) T - 1G ] is

.

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

mapping ( 1 / c ) + - GJ , we find that ( 1 / c ) T - 1G ] is

**similar**to J , so that G is**similar**to J . Q . E . D . 3 . The Friedrichs ' Method for the Discrete Spectrum XX . 2.

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero