## Linear Operators, Part 2 |

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Page 898

If E is the resolution of the

of complex numbers , then EDT = TE ( 8 ) , 0 ( T8 ) ÇJ , where To is the restriction

of T to E ( 8 ) Ý . 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 EDT = TE ( 8 ) , 0 ( T8 ) ÇJ , where To is the restriction

of T to E ( 8 ) Ý . Proof . The first statement follows from Theorem 1 ( ii ) . Now for ...

Page 920

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

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

equivalent . Let E and Ể be the resolutions of the

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

By induction on ( J1 ) , we can readily show that a formal

002 = C ( x ) 201202 + CJ . J . aj ( x ) a ) , HI < \ J , 1 + lJA with suitable coefficients

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

By induction on ( J1 ) , we can readily show that a formal

**identity**( 1 ) DJ1C ( x )002 = C ( x ) 201202 + CJ . J . aj ( x ) a ) , HI < \ J , 1 + lJA with suitable coefficients

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

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

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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