## 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 2118

A generalized scalar operator Te B ( X ) is said to be

A generalized scalar operator Te B ( X ) is said to be

**regular**if it has a**regular**spectral distribution . Although it is not known whether or not every generalized scalar operator is**regular**( unless the spectrum is sufficiently " thin ...Page 2158

The above statement is what was actually proved in the preceding proof . Q.E.D. 10 LEMMA ( B , G ) . If the set of points

The above statement is what was actually proved in the preceding proof . Q.E.D. 10 LEMMA ( B , G ) . If the set of points

**regular**relative to T is dense on To , then every closed subinterval of I , whose end points are**regular**relative ...Page 2160

I – T ) y = 0 and a vector a y in the closure of ( 1.1 - T ) X . Since 1o is interior to an interval of constancy relative to T , it is therefore a

I – T ) y = 0 and a vector a y in the closure of ( 1.1 - T ) X . Since 1o is interior to an interval of constancy relative to T , it is therefore a

**regular**point relative to T. Q.E.D. 14 LEMMA ( G ) . If X is reflexive and if the ...### 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