## Linear Operators: Spectral operators |

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The unique countably additive resolution of the

in the plane which is determined by a spectral operator T is called the resolution

of the

The unique countably additive resolution of the

**identity**defined on the Borel setsin the plane which is determined by a spectral operator T is called the resolution

of the

**identity**for T . 10 THEOREM . Let I = E1 + . . . + En where E1 , . . . , En are ...Page 2094

12 ) that if X is a weakly complete B - space , then any prespectral operator is

automatically spectral , and so has a unique resolution of the

and Dowson [ 1 ] have considered prespectral operators in some detail and have

...

12 ) that if X is a weakly complete B - space , then any prespectral operator is

automatically spectral , and so has a unique resolution of the

**identity**. Berksonand Dowson [ 1 ] have considered prespectral operators in some detail and have

...

Page 2242

The projection valued measure E is said to be the resolution of the

13 LEMMA . An unbounded spectral operator of scalar type in the sense of

Definition 12 is a spectral operator in the sense of Definition 1 . Moreover , the ...

The projection valued measure E is said to be the resolution of the

**identity**for T .13 LEMMA . An unbounded spectral operator of scalar type in the sense of

Definition 12 is a spectral operator in the sense of Definition 1 . Moreover , the ...

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