## Linear Operators, Part 1 |

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Page 69

Hence bounded sets are

from the preceding lemma . Q.E.D. 29 COROLLARY . A reflexive space is

complete . ' PROOF . If { xn } is a sequence in a reflexive space X for which lim x *

x ...

Hence bounded sets are

**weakly**sequentially compact . The converse followsfrom the preceding lemma . Q.E.D. 29 COROLLARY . A reflexive space is

**weakly**complete . ' PROOF . If { xn } is a sequence in a reflexive space X for which lim x *

x ...

Page 507

Let ( S , E , u ) be a o - finite positive measure space , and let T be a

compact operator on L ( S , E , u ) to a separable subset of the B - space X. Then

there exists a u - essentially unique bounded measurable function x ( • ) on S to a

...

Let ( S , E , u ) be a o - finite positive measure space , and let T be a

**weakly**compact operator on L ( S , E , u ) to a separable subset of the B - space X. Then

there exists a u - essentially unique bounded measurable function x ( • ) on S to a

...

Page 540

A very incisive discussion of

given by Grothendieck [ 4 ] who proved Theorems 7.4—7.6 by other means .

Grothendieck showed there is a one - to - one correspondence between

A very incisive discussion of

**weakly**compact operators with domain C ( S ) wasgiven by Grothendieck [ 4 ] who proved Theorems 7.4—7.6 by other means .

Grothendieck showed there is a one - to - one correspondence between

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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