## Linear Operators: General theory |

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Page 72

1.11) is a

a Cauchy sequence in X/3, define a subsequence for which \xk— £*+1+3l < 2~*>

k = 1,2,..., and show that a Cauchy sequence in X can be chosen which maps ...

1.11) is a

**B**-**space**(or an F-space) with the metric \x+Q\ = inf \x+z\. «3 (Hint: Givena Cauchy sequence in X/3, define a subsequence for which \xk— £*+1+3l < 2~*>

k = 1,2,..., and show that a Cauchy sequence in X can be chosen which maps ...

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 X. 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 X. 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 ^-convergent sequence in X* is actually X**-

convergent, and that if ?) is a separable

...

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

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

convergent, and that if ?) is a separable

**B**-**space**, then any operator in B(X, ?)) is...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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