## Linear Operators: Spectral operators |

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Page 1930

3 DEFINITION . A spectral measure E is said to be countably additive if for each x

* in X * and each x in X the scalar set function x * E ( • ) x is countably additive on

the

3 DEFINITION . A spectral measure E is said to be countably additive if for each x

* in X * and each x in X the scalar set function x * E ( • ) x is countably additive on

the

**domain**of E . + 4 COROLLARY . If the**domain**of a countably 1930 XV . 2 .Page 2087

Then ( i ) The operator Ag + B with

generator of a strongly continuous semi - group S ( t ) , t 20 , of bounded linear

operators in HP and S ( t ) has a strongly analytic extension to a semi - group ...

Then ( i ) The operator Ag + B with

**domain**( p ) T ( 29 ) ( RN ) is the infinitesimalgenerator of a strongly continuous semi - group S ( t ) , t 20 , of bounded linear

operators in HP and S ( t ) has a strongly analytic extension to a semi - group ...

Page 2256

where C , is a finite collection of closed Jordan curves bounding a

containing the union of o ( T ) and a neighborhood of infinity , Cį being oriented in

the customary positive sense of complex variable theory . The curves C of the ...

where C , is a finite collection of closed Jordan curves bounding a

**domain**D ,containing the union of o ( T ) and a neighborhood of infinity , Cį being oriented in

the customary positive sense of complex variable theory . The curves C of the ...

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