## Linear Operators: General theory |

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Page 89

Occasionally it is necessary to consider metric

complete . ... 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

.

Occasionally it is necessary to consider metric

**linear spaces**which are notcomplete . ... 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

.

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

scalars Oy , . . . Con with the norm 1x1 = sup lait isisn 4 . The space l , is defined

for 1 Sp < oo as the

the ...

The space i " is the

**linear space**of all ordered n - tuples x = [ 0 ] , . . . , On ] ofscalars Oy , . . . Con with the norm 1x1 = sup lait isisn 4 . The space l , is defined

for 1 Sp < oo as the

**linear space**of all sequences x = { an } of scalars for whichthe ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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