## Linear Operators, Part 1 |

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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 I ' " is the

, an with the norm = sup lail . 1 Sisn 4 . The space 1 , is defined for 1 p < oo as the

The space I ' " is the

**linear space**of all ordered n - tuples [ , . an ] of scalars Oj , . ..., an with the norm = sup lail . 1 Sisn 4 . The space 1 , is defined for 1 p < oo as the

**linear space**of all sequences x = { an } of scalars for which the norm | x ) = { 1 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

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