## Linear Operators: Spectral operators |

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strongly closed if and only if it is

strongly closed if and only if it is

**complete**in the sense of the following definition . 1 DEFINITION . A Boolean algebra B of projections in a B - space X is said to be**complete**( o -**complete**) as an abstract Boolean algebra if each ...Page 2204

This means that for every Borel set e in , there is a projection E ( e ) in B with A ( e ) = E ( e ) * , and thus the proof is

This means that for every Borel set e in , there is a projection E ( e ) in B with A ( e ) = E ( e ) * , and thus the proof is

**complete**. Q.E.D. 10 COROLLARY . A Boolean algebra of projections in a B - space is o -**complete**if and only ...Page 2217

Let B be a o -

Let B be a o -

**complete**Boolean algebra of projections in a B - space X , and let B , be its strong closure . By Lemma 3 , B is bounded and thus B , is also a bounded Boolean algebra of projections in X. Suppose that B , is not**complete**...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function 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