## Linear Operators: General theory |

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Page 89

Completion of spaces . In the definitions of F - and B - spaces , we required the

spaces to be complete in their metric topology . Occasionally it is necessary to

consider metric

following ...

Completion of spaces . In the definitions of F - and B - spaces , we required the

spaces to be complete in their metric topology . Occasionally it is necessary to

consider metric

**linear spaces**which are not complete . In such cases , thefollowing ...

Page 91

Thus every complete linear metric space can be metrized to be an F - space .

Further , a normed

equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in

Thus every complete linear metric space can be metrized to be an F - space .

Further , a normed

**linear space**is a B - space provided it is complete under someequivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in

**linear spaces**.Page 239

The space Ime is the

scalars Qi , . . . , Chon with the norm \ w \ = sup laila 1Sisn 4 . The space l , is

defined for 1 sp < oo as the

which ...

The space Ime is the

**linear space**of all ordered n - tuples x = [ 0 , 1 , . . . , cn ] ofscalars Qi , . . . , Chon with the norm \ w \ = sup laila 1Sisn 4 . The space l , is

defined for 1 sp < oo as the

**linear space**of all sequences x = { en } of scalars forwhich ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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