## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2194

Strongly Closed Algebras and Complete

attempt will be made to characterize the strong closure of a commutative algebra

of spectral operators . It has been observed ( cf . VI . 1 . 5 ) that a convex set in the

...

Strongly Closed Algebras and Complete

**Boolean Algebras**In this section anattempt will be made to characterize the strong closure of a commutative algebra

of spectral operators . It has been observed ( cf . VI . 1 . 5 ) that a convex set in the

...

Page 2195

A

complete ) as an abstract

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

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 subset ( sequence ) of B has agreatest lower bound and a least upper bound in B . The

**Boolean algebra**B is ...Page 2217

Let B be a o - complete

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

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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