## 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 2110

Thus the scalar operators in such spaces are

Thus the scalar operators in such spaces are

**limits**in the strong operator topology of finite dimensional operators . ... Although he considered closed operators , we shall**limit**our attention to operators Te B ( x ) , where X is a ...Page 2177

At the same time , various sufficient conditions that the uniform , weak , and strong

At the same time , various sufficient conditions that the uniform , weak , and strong

**limits**of sequences of commuting ... Finally , in Section 4 , will be found two results concerning the strong**limit**of a sequence of non - commuting ...Page 2219

Strong

Strong

**Limits**of Spectral Operators : Non - Commutative Case In this section conditions will be given to insure that the strong**limit**T = lim , Te of a generalized sequence { T , } of scalar type spectral operators is itself a scalar ...### 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