## 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

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 ...

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. 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

Nelson Dunford, Jacob T. Schwartz. 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 Y * is Y - compact ...### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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