## Linear Operators, Part 1 |

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Page 244

prototype of all n-dimensional normed linear spaces, and hence it should be

observed first that E” is a B-space. The Minkowski inequality (III.3.3) shows E" to

be a ...

**Finite Dimensional**Spaces The space E", as will be seen presently, is theprototype of all n-dimensional normed linear spaces, and hence it should be

observed first that E” is a B-space. The Minkowski inequality (III.3.3) shows E" to

be a ...

Page 245

An n-dimensional B-space is equivalent to E”. 4 CoROLLARY. Every linear

operator on a

b1, ..., b.} be a Hamel basis for the

that ...

An n-dimensional B-space is equivalent to E”. 4 CoROLLARY. Every linear

operator on a

**finite dimensional**normed linear space is continuous. - PRoof. Let (b1, ..., b.} be a Hamel basis for the

**finite dimensional**normed linear space & sothat ...

Page 246

Thus the

the

3.19), the

...

Thus the

**dimension**of 3:* is n. Conversely, let the**dimension**of to be**finite**. Thenthe

**dimension**of 3:** is**finite**, and, since 3. is equivalent to a subspace of 3:** (II.3.19), the

**dimension**of 3 is**finite**. Hence, from the first part of this proof, 3 and 3%...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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