## Linear Operators: General theory |

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Page 72

11 ) is a

Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which XX - Xk

+ 1 + 81 < 2 - k , k = 1 , 2 , . . . , and show that a Cauchy sequence in X can be ...

11 ) is a

**B**-**space**( or an F - space ) with the metric 18 + 3 ) = inf ( x + 21 . 2€3 (Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which XX - Xk

+ 1 + 81 < 2 - k , k = 1 , 2 , . . . , and show that a Cauchy sequence in X can be ...

Page 89

In the definitions of F - and

their metric topology . ... Then X is isomorphic and isometric with a dense linear

subspace of an F - space Ž . The space X is uniquely determined up to isometric

...

In the definitions of F - and

**B**-**spaces**, we required the spaces to be complete intheir metric topology . ... Then X is isomorphic and isometric with a dense linear

subspace of an F - space Ž . The space X is uniquely determined up to isometric

...

Page 398

Let S be a Stone space and X = C ( S ) the real continuous functions .

Grothendieck [ 4 ; p . 168 ] showed that every X - convergent sequence in X * is

actually X * * - convergent , and that if Y is a separable

operator in B ( X ...

Let S be a Stone space and X = C ( S ) the real continuous functions .

Grothendieck [ 4 ; p . 168 ] showed that every X - convergent sequence in X * is

actually X * * - convergent , and that if Y is a separable

**B**-**space**, then anyoperator in B ( X ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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