## Linear Operators: Spectral theory |

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Results 1-3 of 92

Page 898

If E is the resolution of the

of complex numbers , then E ( 8 ) T = TE ( 8 ) , ( Ts ) CJ , where To is the

restriction of T to E ( 8 ) H . Proof . The first statement follows from Theorem 1 ( ii )

.

If E is the resolution of the

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

restriction of T to E ( 8 ) H . Proof . The first statement follows from Theorem 1 ( ii )

.

Page 920

Under this assumption it will be shown that there is an ordered representation of

H onto - , L , lēm , ) relative to T . It will follow from Theorem 10 that U and Ở are

equivalent . Let E and Ể be the resolutions of the

Under this assumption it will be shown that there is an ordered representation of

H onto - , L , lēm , ) relative to T . It will follow from Theorem 10 that U and Ở are

equivalent . Let E and Ể be the resolutions of the

**identity**for T and † respectively .Page 1717

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

= C ( x ) DJ1202 + £ C1 , 1 , 23 ( x ) 20 , IJI < \ J , / + lJ2 with suitable coefficients

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

...

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

**identity**( 1 ) DJ1C ( x ) dde= C ( x ) DJ1202 + £ C1 , 1 , 23 ( x ) 20 , IJI < \ J , / + lJ2 with suitable coefficients

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

**identities**of the type...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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