## 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 1917

This purely formal argument inspires us to study the

indeed it develops that if the difference T ' – T satisfies suitable hypotheses , this

This purely formal argument inspires us to study the

**limit**appearing above , andindeed it develops that if the difference T ' – T satisfies suitable hypotheses , this

**limit**will exist in the strong topology and will have the properties which formal ...Page 2219

Strong

conditions will be given to insure that the strong

sequence { Ta } of scalar type spectral operators is itself a scalar type spectral ...

Strong

**Limits**of Spectral Operators : Non - Commutative Case In this sectionconditions will be given to insure that the strong

**limit**T = lim , Tą of a generalizedsequence { Ta } of scalar type spectral operators is itself a scalar type spectral ...

Page 2454

Q . E . D . The error enters , of course , in the implicit assumption that U - v has a

by arguing more carefully , we can extract a kernel of truth from the erroneous ...

Q . E . D . The error enters , of course , in the implicit assumption that U - v has a

**limit**U . v for all v in Hilbert space . However , by adding suitable hypotheses andby arguing more carefully , we can extract a kernel of truth from the erroneous ...

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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