Linear Operators, Part 1 |
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Page 91
admits an equivalent metric under which it is complete , then G admits an
invariant metric and is complete under each invariant metric . Thus every
complete linear metric space can be metrized to be an F - space . Further , a
normed linear ...
admits an equivalent metric under which it is complete , then G admits an
invariant metric and is complete under each invariant metric . Thus every
complete linear metric space can be metrized to be an F - space . Further , a
normed linear ...
Page 311
Proof . Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems
6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is
equivalent to C ( S . ) . Theorem 5.1 shows that there is an isometric isomorphism
æ ...
Proof . Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems
6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is
equivalent to C ( S . ) . Theorem 5.1 shows that there is an isometric isomorphism
æ ...
Page 347
( b ) Show that L ( S , E , u ) is equivalent to l , if and only if there exists a
countable collection of atoms of finite measure { En } in such that every
measurable subset of S - u - En is either an atom of infinite measure or a null set .
50 Show that no ...
( b ) Show that L ( S , E , u ) is equivalent to l , if and only if there exists a
countable collection of atoms of finite measure { En } in such that every
measurable subset of S - u - En is either an atom of infinite measure or a null set .
50 Show that no ...
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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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