## 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 1965

This enables us to consider the B * -

This enables us to consider the B * -

**algebra**C ( S ) of all bounded continuous complex functions on S as a B * -subalgebra of eBIS , E ) , for if e ( 8 ) = e , then 8 is dense in S and hence ( 16 ) sup lā ( 8 ) = e - ess sup la ( s ) ...Page 2194

Let A , be the

Let A , be the

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

28 other sections not shown

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### Common terms and phrases

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