## Linear Operators: Spectral theory |

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Results 1-3 of 94

Page 898

If E is the resolution of the

of complex numbers , then E ( S ) T = TE ( 8 ) , 0 ( T8 ) CJ , where To is the

restriction of T to E ( S ) 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 ( S ) T = TE ( 8 ) , 0 ( T8 ) CJ , where To is the

restriction of T to E ( S ) 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 = Lzlēm , ī ) relative to T . It will follow from Theorem 10 that U and Ở are

equivalent . Let E and Ę be the resolutions of the

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

H onto = Lzlēm , ī ) relative to T . It will follow from Theorem 10 that U and Ở are

equivalent . Let E and Ę be the resolutions of the

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

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

DJ2 = C ( x ) 212213 + CJ , j , aj ( x ) a ) , IJI < \ J11 + J2L with suitable coefficients

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

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

**identity**( 1 ) 2011 C ( x )DJ2 = C ( x ) 212213 + CJ , j , aj ( x ) a ) , IJI < \ J11 + J2L with suitable coefficients

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

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

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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