## 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 2169

uniform limit of analytic functions , it follows that this map is also a homomorphism

on the algebra of continuous functions . To see that it is a homomorphism on the

algebra of

uniform limit of analytic functions , it follows that this map is also a homomorphism

on the algebra of continuous functions . To see that it is a homomorphism on the

algebra of

**bounded Borel**functions , note that for a fixed continuous function g ...Page 2233

By virtue of the equation f ( T | E ( e ) X ) x = f ( T | E ( ē ) X ) , which has been

established for x in E ( e ) X n Esē ) X , we may define a single valued linear

operator Qo on Ue E ( e ) X , where e varies over the family of

whose ...

By virtue of the equation f ( T | E ( e ) X ) x = f ( T | E ( ē ) X ) , which has been

established for x in E ( e ) X n Esē ) X , we may define a single valued linear

operator Qo on Ue E ( e ) X , where e varies over the family of

**bounded Borel**setswhose ...

Page 2262

Furthermore , if equation ( 5 ) holds for each function in a uniformly bounded

pointwise convergent sequence { fn } , then it follows from ( 4 ) that it holds for the

limit function f = limfn . + Hence ( 5 ) holds if f is any

Furthermore , if equation ( 5 ) holds for each function in a uniformly bounded

pointwise convergent sequence { fn } , then it follows from ( 4 ) that it holds for the

limit function f = limfn . + Hence ( 5 ) holds if f is any

**bounded Borel**function ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero