## Linear Operators: General theory |

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Page 40

For if I is maximal , then R / I is a commutative ring with

ideals ; by what we showed earlier R / I is a field . Conversely , if R / I is a field , it

contains no ideals and hence R has no ideals properly containing I . If R is a ring

...

For if I is maximal , then R / I is a commutative ring with

**unit**which has no properideals ; by what we showed earlier R / I is a field . Conversely , if R / I is a field , it

contains no ideals and hence R has no ideals properly containing I . If R is a ring

...

Page 458

5 If the closed

finite number of extremal points , then X is not isometrically isomorphic to the

conjugate of any B - space . 6 Let S be a topological space , and let C ( S ) be the

B ...

5 If the closed

**unit**sphere of an infinite dimensional B - space X contains only afinite number of extremal points , then X is not isometrically isomorphic to the

conjugate of any B - space . 6 Let S be a topological space , and let C ( S ) be the

B ...

Page 485

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 8 THEOREM . (

Gantmacher ) An operator in B ( X , Y ) is weakly compact if and only if its adjoint

is weakly compact . PROOF . Let T be weakly compact . Since the closed

sphere S * of ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 8 THEOREM . (

Gantmacher ) An operator in B ( X , Y ) is weakly compact if and only if its adjoint

is weakly compact . PROOF . Let T be weakly compact . Since the closed

**unit**sphere S * of ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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