## 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 consists of all bounded linear operators in ...Page 2361

Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show that F * ( a ) = ( ( T + P ) * — XI ) -18 * is

Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show that F * ( a ) = ( ( T + P ) * — XI ) -18 * is

**uniformly**bounded for ...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 .### 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