## 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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Results 1-3 of 47

Page 1943

... o ( T ) in its interior and such that f is analytic within and on C . Then we have $

( T ) = 2 i S . HCE ) R ( E ; T ' ) dę and it follows from Lemma 2 that ( 0 ) $ 29 = 3 . r

" / 10 lute , ce ) . the series converging in the

... o ( T ) in its interior and such that f is analytic within and on C . Then we have $

( T ) = 2 i S . HCE ) R ( E ; T ' ) dę and it follows from Lemma 2 that ( 0 ) $ 29 = 3 . r

" / 10 lute , ce ) . the series converging in the

**uniform**topology of operators .Page 2163

The proof will involve Riemann integrals of the type ( i ) F ( 5 ) E ( dt ) , O ( T ) ( ii )

where E is the resolution of the identity for T and F is an operator valued function

defined on o ( T ) continuous in the

The proof will involve Riemann integrals of the type ( i ) F ( 5 ) E ( dt ) , O ( T ) ( ii )

where E is the resolution of the identity for T and F is an operator valued function

defined on o ( T ) continuous in the

**uniform**operator topology , and for which F ...Page 2283

Then a projection E in B has finite

in B * has finite

* satisfy the countable chain condition . Also since each projection is the union ...

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 . Also since each projection is the union ...

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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