## 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 1928

Terminology and Preliminary Notions The concepts of a Boolean algebra of

Terminology and Preliminary Notions The concepts of a Boolean algebra of

**projections**, a spectral measure , an integral with respect to a spectral measure ...Page 2199

If the strongly closed bounded Boolean algebra B of

If the strongly closed bounded Boolean algebra B of

**projections**is not complete , there is , by the preceding lemma , a vector x and an increasing ...Page 2218

If a generalized sequence of

If a generalized sequence of

**projections**in a o - complete Boolean ... in a B - space converges weakly to a**projection**, then it converges strongly .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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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