## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1930

+ 2 DEFINITION . If Eis a Boolean algebra of subsets of the complex plane which

contains the void set and the whole plane , in short , if is a field of sets in the

complex plane , then a spectral measure E on is called a resolution of the

( or ...

+ 2 DEFINITION . If Eis a Boolean algebra of subsets of the complex plane which

contains the void set and the whole plane , in short , if is a field of sets in the

complex plane , then a spectral measure E on is called a resolution of the

**identity**( or ...

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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