## Linear Operators: Spectral operators |

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Page 2147

Conversely , let the bounded

C ) . Then , by Theorem 3 . 11 and Lemma 3 , T is a spectral operator of class ( S (

T ) , X * ) with a resolution of the identity which is countably additive in the ...

Conversely , let the bounded

**linear operator**T satisfy conditions ( A ) , ( B ) , and (C ) . Then , by Theorem 3 . 11 and Lemma 3 , T is a spectral operator of class ( S (

T ) , X * ) with a resolution of the identity which is countably additive in the ...

Page 2162

If the bounded

and ( G ) then , by Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of

Theorem 4 . 5 , to prove the present theorem it suffices to show that T has

property ...

If the bounded

**linear operator**T in a weakly complete space has properties ( B )and ( G ) then , by Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of

Theorem 4 . 5 , to prove the present theorem it suffices to show that T has

property ...

Page 2400

The basic idea of Friedrichs ' method may be expressed heuristically as follows .

Let X be a B - space , and let T be a

...

The basic idea of Friedrichs ' method may be expressed heuristically as follows .

Let X be a B - space , and let T be a

**linear operator**in X ; let K be a second**linear****operator**in X which is , in a sense to be made precise below , very small relative...

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