## 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

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 isomorphism . If X is a

normed linear space , then X is a

as ...

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 isomorphism . If X is a

normed linear space , then X is a

**B**-**space**. The proof of this theorem proceedsas ...

Page 258

Nelson Dunford, Jacob T. Schwartz. It is clear that B ( S ) is a normed linear

space . To see that it is complete and hence a

Cauchy sequence in B ( s ) . Then for each ε > 0 there is an m ( € ) with \ n - Imi < ε

for n ...

Nelson Dunford, Jacob T. Schwartz. It is clear that B ( S ) is a normed linear

space . To see that it is complete and hence a

**B**-**space**, suppose that { fn } is aCauchy sequence in B ( s ) . Then for each ε > 0 there is an m ( € ) with \ n - Imi < ε

for n ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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