## Linear Operators: Spectral operators |

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Page 2194

It follows from Theorem 10 that A , is a full

operators which is equivalent to EB ( 1 , 3 ) . It follows from the definition of the

integral that A , 9 A ( B ) . On the other hand , every

Thus A ...

It follows from Theorem 10 that A , is a full

**algebra**of scalar type spectraloperators which is equivalent to EB ( 1 , 3 ) . It follows from the definition of the

integral that A , 9 A ( B ) . On the other hand , every

**projection**E ( 8 ) in B is in Aį .Thus A ...

Page 2217

Let B be a o - complete Boolean

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

Boolean

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 .Page 2218

Every operator in the weakly closed operator

operator of scalar type and the

spectral operator of scalar type . Proof . Since a spectral operator of scalar type is

...

Every operator in the weakly closed operator

**algebra**generated by a spectraloperator of scalar type and the

**projections**in its resolution of the identity is aspectral operator of scalar type . Proof . Since a spectral operator of scalar type is

...

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