## Linear Operators: Spectral operators |

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Page 1934

PROOF . Using Theorem 2 , we see that if o ( x ) is void , then x ( 5 ) is

everywhere defined , single valued , and hence entire . Since , by VII . 3 . 4 , lim x

* x ( $ ) = lim x * R ( Š ; T ) x = 0 , Š→ 00 $ 0 it is

and all x * e ...

PROOF . Using Theorem 2 , we see that if o ( x ) is void , then x ( 5 ) is

everywhere defined , single valued , and hence entire . Since , by VII . 3 . 4 , lim x

* x ( $ ) = lim x * R ( Š ; T ) x = 0 , Š→ 00 $ 0 it is

**seen**that x * x ( $ ) = 0 for all §and all x * e ...

Page 2163

8 , it is

| - TĖ Ž ( PE ) – FLERE ( 0 , 05 ) SK sup | F ( $ i ) – F ( $ ) , where the supremum is

taken over those i and j for which 0 ; 0 ; is not void . If by the norm | | is ...

8 , it is

**seen**that , for some constant K , 11 = 1 j = 1 Ë FLEJE ( 6 . ) – Ë FLEJE ( 0 )| - TĖ Ž ( PE ) – FLERE ( 0 , 05 ) SK sup | F ( $ i ) – F ( $ ) , where the supremum is

taken over those i and j for which 0 ; 0 ; is not void . If by the norm | | is ...

Page 2479

Let Q be the projection of H ' onto its subspace Hı , and put V = V2Q . Plainly , V is

symmetric . The operator V ( il – H2 ) - 1 = V2Q ( il – H2 ) - 1 = V2 ( il – H2 ) - " Q is

Let Q be the projection of H ' onto its subspace Hı , and put V = V2Q . Plainly , V is

symmetric . The operator V ( il – H2 ) - 1 = V2Q ( il – H2 ) - 1 = V2 ( il – H2 ) - " Q is

**seen**to be compact by use of Corollary V1 . 5 . 5 , and the operator ( il – H ) ...### What people are saying - Write a review

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