## 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 2141

Let { und and { vn } be as in Definition 7 , and let { în } and { ūn } be

Let { und and { vn } be as in Definition 7 , and let { în } and { ūn } be

**sequences**of closed sets in S 2 ( T ) such that ûn So , vn Sö ' , and ūn x = lim { E ( vn ) + Elžn ) x } , = X e X. no Since the**sequence**{ E ( vn ) + E ( un ) ...Page 2197

Let B be a complete ( o - complete ) Boolean algebra of projections in the B - space X and let { Ex } be a monotone generalized

Let B be a complete ( o - complete ) Boolean algebra of projections in the B - space X and let { Ex } be a monotone generalized

**sequence**( a monotone**sequence**) in B. Then , if { Ex } is increasing , lim Exx = ( Y Ec ) , = XeX , a a a a ...Page 2218

If a generalized

If a generalized

**sequence**of projections in a o - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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