## 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 2144

It clearly preserves finite disjoint unions , takes complements into complements , is countably additive in the X

It clearly preserves finite disjoint unions , takes complements into complements , is countably additive in the X

**topology**of X * , and is bounded .Page 2203

To see this , note that sets of the form { ^ || ( T - 1A ) ( 0 ) | < a } , with A in A ( B ) form , by definition , a subbasis for the

To see this , note that sets of the form { ^ || ( T - 1A ) ( 0 ) | < a } , with A in A ( B ) form , by definition , a subbasis for the

**topology**of 4 ...Page 2278

... to be the smallest cardinal power of a set A of vectors such that E * X * is spanned in the X -

... to be the smallest cardinal power of a set A of vectors such that E * X * is spanned in the X -

**topology**by the manifolds { N ( ** ) | ** € A } .### 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