## Linear operators: Spectral operators |

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Page 2194

The final statement follows from Theorem XV.4.5. Q.E.D. 3. Strongly Closed

Algebras and Complete

to characterize the strong closure of a commutative algebra of spectral operators.

The final statement follows from Theorem XV.4.5. Q.E.D. 3. Strongly Closed

Algebras and Complete

**Boolean Algebras**In this section an attempt will be madeto characterize the strong closure of a commutative algebra of spectral operators.

Page 2195

A

complete) as an abstract

greatest lower bound and a least upper bound in B. The

said to ...

A

**Boolean algebra**B of projections in a S-space X is said to be complete (a-complete) as an abstract

**Boolean algebra**if each subset (sequence) of B has agreatest lower bound and a least upper bound in B. The

**Boolean algebra**B issaid to ...

Page 2217

Let B be a cr-complete

be its strong closure. By Lemma 3, B is bounded and thus Bx is also a bounded

...

Let B be a cr-complete

**Boolean algebra**of projections in a .B-space X, and let Bxbe its strong closure. By Lemma 3, B is bounded and thus Bx is also a bounded

**Boolean algebra**of projections in X. Suppose that .Bj is not complete. By Lemma...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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