## Linear Operators: General theory |

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Page 425

A B - space is reflexive if and only if its closed unit

topology . PROOF . Let X be a reflexive B - space , and let z be the natural

embedding of X onto X * * . Then x and x - l are isometries , and z maps the

closed unit ...

A B - space is reflexive if and only if its closed unit

**sphere**is compact in the weaktopology . PROOF . Let X be a reflexive B - space , and let z be the natural

embedding of X onto X * * . Then x and x - l are isometries , and z maps the

closed unit ...

Page 458

5 If the closed unit

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

Since the closed unit

If S , S * * are the closed unit

natural embedding of X into X * * , then by Theorem V . 4 . 5 , xS is X * - dense in

S ...

Since the closed unit

**sphere**S * of Y * is Y - compact ( V . 4 . 2 ) , it follows from ...If S , S * * are the closed unit

**spheres**in X , X * * , respectively , and if ~ is thenatural embedding of X into X * * , then by Theorem V . 4 . 5 , xS is X * - dense in

S ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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