Linear Operators: Spectral operators |
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Page 2094
Berkson and Dowson [ 1 ] have considered prespectral operators in some detail
and have obtained a number of results concerning them . They show that if T is
spectral , then 7 * has a unique resolution of the identity of class ( X ) ; moreover ,
if ...
Berkson and Dowson [ 1 ] have considered prespectral operators in some detail
and have obtained a number of results concerning them . They show that if T is
spectral , then 7 * has a unique resolution of the identity of class ( X ) ; moreover ,
if ...
Page 2115
Moreover , if T and U are decomposable , then X1 ( F ) = xy ( F ) for all closed sets
F if and only if T and U are quasi - nilpotent equivalent . If T is a spectral operator
and T and U are quasi - nilpotent equivalent , then U is a spectral operator .
Moreover , if T and U are decomposable , then X1 ( F ) = xy ( F ) for all closed sets
F if and only if T and U are quasi - nilpotent equivalent . If T is a spectral operator
and T and U are quasi - nilpotent equivalent , then U is a spectral operator .
Page 2356
Then by Definition XVIII . 2 . 8 , a vector x in E ( oo ) X is in D ( $ ( T ) ) if and only if
it is in D ( F ( S ) ) , and , moreover f ( T ) x = f ( S ) x , for each analytic function f
defined on o ( T ) and for x e E ( 0 . ) X . In particular , x is in D ( T ' ) if and only if x
...
Then by Definition XVIII . 2 . 8 , a vector x in E ( oo ) X is in D ( $ ( T ) ) if and only if
it is in D ( F ( S ) ) , and , moreover f ( T ) x = f ( S ) x , for each analytic function f
defined on o ( T ) and for x e E ( 0 . ) X . In particular , x is in D ( T ' ) if and only if x
...
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Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Part | 1950 |
Copyright | |
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