Linear Operators, Part 1 |
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Page 412
The linear functional f separates the subsets M and N of X if and only if it
separates the subsets M - N and { 0 } of X. The proof is elementary , and is left to
the reader . In dealing with subspaces , it is often convenient to make use of the
following ...
The linear functional f separates the subsets M and N of X if and only if it
separates the subsets M - N and { 0 } of X. The proof is elementary , and is left to
the reader . In dealing with subspaces , it is often convenient to make use of the
following ...
Page 418
If p and q are distinct points of a locally convex linear topological space X , there
is a continuous linear functional f ... tz ) have the same continuous linear
functionals , then a convex set is closed in ( X , 7ı ) if and only if it is closed in ( X ,
T2 ) ...
If p and q are distinct points of a locally convex linear topological space X , there
is a continuous linear functional f ... tz ) have the same continuous linear
functionals , then a convex set is closed in ( X , 7ı ) if and only if it is closed in ( X ,
T2 ) ...
Page 421
Let X be a linear space , and let T be a total subspace of X * . Then the linear
functionals on X which are continuous in the I topology are precisely the
functionals in l . The proof of Theorem 9 will be based on the following lemma .
10 LEMMA .
Let X be a linear space , and let T be a total subspace of X * . Then the linear
functionals on X which are continuous in the I topology are precisely the
functionals in l . The proof of Theorem 9 will be based on the following lemma .
10 LEMMA .
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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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