## Linear Operators: Spectral operators |

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Page 2209

The weakly

The weakly

**closed**operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly**closed**algebra generated by B. PROOF . It is clear that every element in ...Page 2214

By Corollary VI.1.5 , the weakly

By Corollary VI.1.5 , the weakly

**closed**operator algebra W ( B ) generated by B is the same as the strongly**closed**algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It ...Page 2217

Let X ( x ) , X ( 2 ) be the

Let X ( x ) , X ( 2 ) be the

**closed**linear manifolds generated by the sets { Ex | E B } , { Ex | E e Bi } , respectively . Since B , is the strong closure of B , each element Ex with E in B , is contained in X ( x ) and thus X ( x ) 2 X ...### 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 | 1931 |

Copyright | |

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