## 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 838

Ill special

Banach limits, existence and properties, II.4.22-23 (73) Banach theorem, on

convergence of measurable functions, IV. 11.2-3 (332-334) Banach-Stone

theorem, ...

Ill special

**B**-**spaces**, Chap. IV properties, IV.15 Baire category theorem, 1.6.9 (20)Banach limits, existence and properties, II.4.22-23 (73) Banach theorem, on

convergence of measurable functions, IV. 11.2-3 (332-334) Banach-Stone

theorem, ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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