## 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 2098

He based his argument on a

He based his argument on a

**result**for spectral measures due to Lorch [ 1 ] and Mackey [ 4 ] . The proof given here depends on the**result**, due to Sz . - Nagy [ 7 ] , that a bounded Abelian group of operators in a Hilbert space is ...Page 2214

Q.E.D. The preceding material of the present section was largely preliminary to the following basic

Q.E.D. The preceding material of the present section was largely preliminary to the following basic

**result**of Bade , which was described in the introduction . 18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly ...Page 2348

Then the present

Then the present

**result**would follow from Theorem 2.7 , Corollary 2.8 , Theorem 8 , Theorem 13 , and Lemma 15 once we showed that ( using the notations of the hypothesis of Theorem 2.7 ) = 1 dm ? ( [ Am ] + dm ) 2 ( n − 2 ) n < 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