## 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 lett | S M for all te R implies that T is equivalent to a self adjoint operator and

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

**hence**is a scalar type operator ...Page 2308

From this , it follows immediately that S - XI is closed , and

From this , it follows immediately that S - XI is closed , and

**hence**from Lemma XII.1.5 , that ( 8 - XI ) -1 is closed . Since this latter operator is ...Page 2357

then it is clear that L is a bounded operator and that ( 8 - 11 ) - " = ( T – WI ) - ' L .

then it is clear that L is a bounded operator and that ( 8 - 11 ) - " = ( T – WI ) - ' L .

**Hence**V ( P + N ) ( 8 – XI ) -v = P ( S – XI ) - " + N ( S – 21 ) ...### What people are saying - Write a review

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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