## Linear Operators: Spectral operators |

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Page 2125

sets { P ( 8 ) | 8 € D ( P ) } and { P ( 8 ) * 1 8 € D ( P ) } are total on H . It is proved

that every g . s . m . can be extended to a class Do ( P ) of Borel subsets of C

which ...

**Borel sets**and if x , y EH , then + ( P ( 8 ) x , y ) = Ě ( P 8mba , y ) . k = 1 ( iv ) Thesets { P ( 8 ) | 8 € D ( P ) } and { P ( 8 ) * 1 8 € D ( P ) } are total on H . It is proved

that every g . s . m . can be extended to a class Do ( P ) of Borel subsets of C

which ...

Page 2202

4 that there is a spectral measure A in X * defined on the

that XT ( $ ) * = XA ( d ) ) 2 * , x € X , * e ... It will now be shown that , because of

the completeness of B , the operator A ( e ) is , for every

...

4 that there is a spectral measure A in X * defined on the

**Borel sets**in 1 and suchthat XT ( $ ) * = XA ( d ) ) 2 * , x € X , * e ... It will now be shown that , because of

the completeness of B , the operator A ( e ) is , for every

**Borel set**e , the adjoint of...

Page 2233

Let T be a spectral operator with resolution of the identity E , and let f be a

function analytic in an open set U such that E ( U ) ... The operator f ( T ) of

Definition 8 is closed , linear , and independent of the particular sequence of

Let T be a spectral operator with resolution of the identity E , and let f be a

function analytic in an open set U such that E ( U ) ... The operator f ( T ) of

Definition 8 is closed , linear , and independent of the particular sequence of

**Borel sets**used to ...### What people are saying - Write a review

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