## 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 2174

In a Hilbert space the condition that letet S M for all te R implies that T is equivalent to a self adjoint operator and

In a Hilbert space the condition that letet S M for all te R implies that T is equivalent to a self adjoint operator and

**hence**is a scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the ...Page 2308

From this , it follows immediately that S NI is closed , and

From this , it follows immediately that S NI is closed , and

**hence**from Lemma XII.1.5 , that ( 8 - XI ) -1 is closed . Since this latter operator is everywhere defined , it follows by the closed graph theorem ( II.2.4 ) that it is ...Page 2357

then it is clear that L is a bounded operator and that ( S – XI ) - v = ( T – XI ) - " L .

then it is clear that L is a bounded operator and that ( S – XI ) - v = ( T – XI ) - " L .

**Hence**- V - ( P + N ) ( 8 – 21 ) - ° = P ( S – XI ) - " + N ( S – 21 ) -v = P ( T – XI ) - " L + N ( S – XI ) – » is a bounded operator which is ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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