## 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 2179

The uniformly closed

The uniformly closed

**algebra**of operators generated by a bounded Boolean**algebra**of projection operators is a full**algebra**equivalent to the**algebra**of continuous functions on its own space of maximal ideals . PROOF .Page 2194

Let A , be the

Let A , be the

**algebra**of all operators of the form sf ( 2 ) E ( d ) ) where f is E - essentially bounded on o ( s ) . It follows from Theorem 10 that 4 , is a full**algebra**of scalar type spectral operators which is equivalent to EB ( 1 ...Page 2214

By Corollary VI.1.5 , the weakly closed operator

By Corollary VI.1.5 , the weakly closed operator

**algebra**W ( B ) generated by B is the same as the strongly closed**algebra**generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It ...### 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function 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