## Linear Operators: Spectral theory |

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Page 898

If E is the resolution of the

of complex numbers , then E ( ) T = TE ( 8 ) , o ( T8 ) C3 , where To is the

restriction of T to E ( OH . Proof . The first statement follows from Theorem 1 ( ii ) .

Now for ...

If E is the resolution of the

**identity**for the normal operator T and if d is a Borel setof complex numbers , then E ( ) T = TE ( 8 ) , o ( T8 ) C3 , where To is the

restriction of T to E ( OH . Proof . The first statement follows from Theorem 1 ( ii ) .

Now for ...

Page 920

Let E and Ể be the resolutions of the

Corollary 2.7 it is seen that Ể = VEV - 1 and hence that F ( † ) = VF ( T ) V - 1 for

every bounded Borel function F. The mapping W = Ū V of H onto En - 1 Lylēm , û

) is ...

Let E and Ể be the resolutions of the

**identity**for T and † respectively . FromCorollary 2.7 it is seen that Ể = VEV - 1 and hence that F ( † ) = VF ( T ) V - 1 for

every bounded Borel function F. The mapping W = Ū V of H onto En - 1 Lylēm , û

) is ...

Page 1717

By induction on Jil , we can readily show that a formal

= C ( x ) 21212 + Σ C1,1 , ( x ) a ) , NJI < \ J , 1 + 1J21 with suitable coefficients C1,

1 ,, holds for every function Cin C90 ( 1. ) . Making use of

By induction on Jil , we can readily show that a formal

**identity**( 1 ) J01C ( x ) 213= C ( x ) 21212 + Σ C1,1 , ( x ) a ) , NJI < \ J , 1 + 1J21 with suitable coefficients C1,

1 ,, holds for every function Cin C90 ( 1. ) . Making use of

**identities**of the type ...### What people are saying - Write a review

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