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

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Page 1951

Q . E . D 3

E ( o ) with 0 € 7 . PROOF . By

closed twosided ideal in B ( X ) and so the present

Q . E . D 3

**COROLLARY**. If T is compact , then so are S , N , and every projectionE ( o ) with 0 € 7 . PROOF . By

**Corollary**VI . 5 . 5 the compact operators form aclosed twosided ideal in B ( X ) and so the present

**corollary**is immediate .Page 1952

6

0 if 0 € 7 ( respectively SA , = NA , = E ( 0 ) A , = 0 if 0 € 7 ) . 7

spectral operator is of finite type if and only if it is annihilated by some power of its

...

6

**COROLLARY**. If A . T = 0 ( respectively TA , = 0 ) , then A , S = AN = A , E ( 0 ) =0 if 0 € 7 ( respectively SA , = NA , = E ( 0 ) A , = 0 if 0 € 7 ) . 7

**COROLLARY**. Aspectral operator is of finite type if and only if it is annihilated by some power of its

...

Page 2192

This shows that o ( $ ( J ) ) 25 ( 0 ) 2 n 1 ( 8 ) and completes the proof of the

lemma , Q . E . D . 12

complete B - space X . Suppose that A is topologically and algebraically

isomorphic ...

This shows that o ( $ ( J ) ) 25 ( 0 ) 2 n 1 ( 8 ) and completes the proof of the

lemma , Q . E . D . 12

**COROLLARY**. Let A be an algebra of operators in a weaklycomplete B - space X . Suppose that A is topologically and algebraically

isomorphic ...

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