Linear Operators: Spectral theory |
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Page 898
If E is the resolution of the identity for the normal operator T and if d is a Borel set
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 set
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 ) .
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 identity for T and † respectively .
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 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 ) ...
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 ) ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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