## 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 2209

The

The

**uniformly**closed operator algebra generated by a complete Boolean algebra B of projections in a B - space X ... It is clear that every operator in the**uniformly**closed algebra generated by B has the required invariance property .Page 2361

Thus , F * ( a ) is

Thus , F * ( a ) is

**uniformly**bounded for 1 in Un Vi , and hence , by the maximum modulus theorem ... i 2 N , covers the whole plane , with the possible exception of a bounded set , ( F * ( ) | is**uniformly**bounded .Page 2382

We shall now show that the second expression on the right of ( 14 ) converges to zero as lol → 00 , remaining in P + ,

We shall now show that the second expression on the right of ( 14 ) converges to zero as lol → 00 , remaining in P + ,

**uniformly**for 0 St < 0 . Let { qn } be a sequence of functions in C [ 0 , 0 ) , each vanishing outside a bounded ...### 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