## Linear Operators: General theory |

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Page 244

Finite

prototype of all n -

observed first that En is a B - space . The Minkowski inequality ( III.3.3 ) shows En

to be ...

Finite

**Dimensional**Spaces The space En , as will be seen presently , is theprototype of all n -

**dimensional**normed linear spaces , and hence it should beobserved first that En is a B - space . The Minkowski inequality ( III.3.3 ) shows En

to be ...

Page 245

An n -

operator on a finite

{ b , bn } be a Hamel basis for the finite

An n -

**dimensional**B - space is equivalent to E " . 4 COROLLARY . Every linearoperator on a finite

**dimensional**normed linear space is continuous . PROOF . Let{ b , bn } be a Hamel basis for the finite

**dimensional**normed linear space X so ...Page 246

Then the

*** ( II.3.19 ) , the

11 ) of infinite

Then the

**dimension**of X ** is finite , and , since X is equivalent to a subspace of*** ( II.3.19 ) , the

**dimension**of X is finite . ... preliminary discussion in Section IV.11 ) of infinite

**dimensional**F - spaces with zero**dimensional**conjugate spaces .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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