## Linear Operators, Part 2 |

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Page 898

If Eis the resolution of the

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

restriction of T to E ( S ) Y . PROOF . The first statement follows from Theorem 1 (

ii ) .

If Eis 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 ) , o ( T8 ) CJ , where To is the

restriction of T to E ( S ) Y . 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 ma , Lylēn , ū ) relative to T. It will follow from Theorem 10 that U and Ū 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 ma , Lylēn , ū ) relative to T. It will follow from Theorem 10 that U and Ū are

equivalent . Let E and Ể be the resolutions of the

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

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

= C ( x ) 201202 + Σ { x Cj , j , ay ( « ) , JI < \ J11 + lJA ! with suitable coefficients C

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

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

**identity**( 1 ) 2010 ( x ) 2J3= C ( x ) 201202 + Σ { x Cj , j , ay ( « ) , JI < \ J11 + lJA ! with suitable coefficients C

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

**identities**of the type ( 1 ) ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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