## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 93

Page 898

If E is the resolution of the

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

restriction of T to E ( ) . 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 ) , 0 ( T8 ) CJ , where To is the

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

equivalent . Let E and be the resolutions of the

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

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

equivalent . Let E and be the resolutions of the

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

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

= C ( x ) 201 202 + £ C1 , 1 , 2 ; ( x ) , IJI < \ JI + J2L with suitable coefficients C ) , ,

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

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

**identity**( 1 ) 2010 ( x ) 002= C ( x ) 201 202 + £ C1 , 1 , 2 ; ( x ) , IJI < \ JI + J2L with suitable coefficients C ) , ,

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

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

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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