## 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 2283

Then a projection E in B has

Then a projection E in B has

**finite**uniform multiplicity n if and only if its adjoint E * in B * has**finite**uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition .Page 2292

If T is discrete , then ( a ) its spectrum is a denumerable set of points with no

If T is discrete , then ( a ) its spectrum is a denumerable set of points with no

**finite**limit point ; ( b ) the resolvent R ( a ; T ) is compact for every 10 ( T ) ; λ ( c ) every do in o ( T ) is a pole of**finite**order vede ) of the ...Page 2469

Therefore , for each n ε 21 and each € > 0 , the operator Vn.e ) is very smooth and

Therefore , for each n ε 21 and each € > 0 , the operator Vn.e ) is very smooth and

**finite**. If we now choose n = n ( e ) so that IV ( n ) – V * < € / 2 , then choose d = 8 ( e ) so that IV ( 1.0 ) – V ( n ) / * < 8/2 , and put y ( 6 ) ...### 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