## Linear Operators: Spectral operators |

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Page 2194

It has been observed ( cf . VI . 1 . 5 ) that a convex set in the space of all bounded

linear maps between two B - spaces has the same

strong operator topology . Thus the strong and weak operator

It has been observed ( cf . VI . 1 . 5 ) that a convex set in the space of all bounded

linear maps between two B - spaces has the same

**closure**in the weak as in thestrong operator topology . Thus the strong and weak operator

**closures**of an ...Page 2217

Let B be a o - complete Boolean algebra of projections in a B - space X , and let B

, be its strong

Boolean algebra of projections in X . Suppose that B , is not complete .

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 boundedBoolean algebra of projections in X . Suppose that B , is not complete .

Page 2286

If A is the closed densely defined linear map of X into the Hilbert space H of

Lemma 35 , then the

bounded Borel function g on the plane let Š ( g ) denote the

1 .

If A is the closed densely defined linear map of X into the Hilbert space H of

Lemma 35 , then the

**closure**of AQA - 1 is a bounded normal operator . For eachbounded Borel function g on the plane let Š ( g ) denote the

**closure**of AS ( g ) A -1 .

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