Linear Operators, Part 1 |
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Page 419
Nelson Dunford, Jacob T. Schwartz. 2 DEFINITION . Let X be a linear vector
space , and let I be a total subspace of X * . Then the l ' topology of X is the
topology obtained by taking as base all sets of the form N ( p ; A , 8 ) = { 9 ||| ( p ) -
[ ( 9 ) < € ...
Nelson Dunford, Jacob T. Schwartz. 2 DEFINITION . Let X be a linear vector
space , and let I be a total subspace of X * . Then the l ' topology of X is the
topology obtained by taking as base all sets of the form N ( p ; A , 8 ) = { 9 ||| ( p ) -
[ ( 9 ) < € ...
Page 420
Nelson Dunford, Jacob T. Schwartz. in the X * topology if and only if lim , xe = x
weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of
y * , then each element y e Y determines the linear functional f , on X defined by 1
...
Nelson Dunford, Jacob T. Schwartz. in the X * topology if and only if lim , xe = x
weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of
y * , then each element y e Y determines the linear functional f , on X defined by 1
...
Page 477
strong , and the weak operator topologies in B ( X , Y ) . It is evident that the
uniform operator topology is stronger than the strong operator topology , and that
the strong operator topology is stronger than the weak operator topology . With its
...
strong , and the weak operator topologies in B ( X , Y ) . It is evident that the
uniform operator topology is stronger than the strong operator topology , and that
the strong operator topology is stronger than the weak operator topology . With its
...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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