Linear Operators, Part 1 |
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Page 168
Let ( S , E , ) be a positive measure space and G a separable subset of Lp ( S , E ,
u , X ) , where 1 sp < 0. Then there is a set s , in E , a sub o - field & of E ( S ) , and
a closed separable subspace X of X such that the restriction My of u to ; has the ...
Let ( S , E , ) be a positive measure space and G a separable subset of Lp ( S , E ,
u , X ) , where 1 sp < 0. Then there is a set s , in E , a sub o - field & of E ( S ) , and
a closed separable subspace X of X such that the restriction My of u to ; has the ...
Page 426
If X is separable , let { xn } be a countable dense subset of X , and define | ( x * —
y * ) xn | 0 ( 2 * , 4 * ) = Σ n = 1 21 1+ | ( 2 * —Y * ) xml It is easy to verify that the
topology of S * defined by this metric is weaker than the X topology of S * . Hence
...
If X is separable , let { xn } be a countable dense subset of X , and define | ( x * —
y * ) xn | 0 ( 2 * , 4 * ) = Σ n = 1 21 1+ | ( 2 * —Y * ) xml It is easy to verify that the
topology of S * defined by this metric is weaker than the X topology of S * . Hence
...
Page 507
may be noted that the next theorem applies to every continuous linear map of L (
S , E , u ) into a separable reflexive space . 10 THEOREM . Let ( S , E , u ) be a o -
finite positive measure space , and let T be a weakly compact operator on L ( S ...
may be noted that the next theorem applies to every continuous linear map of L (
S , E , u ) into a separable reflexive space . 10 THEOREM . Let ( S , E , u ) be a o -
finite positive measure space , and let T be a weakly compact operator on L ( S ...
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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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