## 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 2257

01 point in o ( R ) , including zero , is contained in an arbitrarily small

01 point in o ( R ) , including zero , is contained in an arbitrarily small

**compact**set open in the relative topology of o ( R ) . Hence , o ( R ) is totally disconnected . It follows by Definition VII.9.3 that Elo ; T ) = E ( 70 ) ...Page 2360

It will also be shown that T- " is

It will also be shown that T- " is

**compact**. From this , ( iii ) , and Theorem VI.5.4 , it will follow that B ( u ) = R ( M ; T + P ) is**compact**for u in V , and i sufficiently large , so that the theorem will be proved .Page 2462

is

is

**compact**. Put C = QR1 , and D R2 , so that V = CD . The operator C is**compact**by Corollary V1.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a**compact**operator in H , and { T , } is a uniformly bounded ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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