## 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

Then the dimension of 3:** is finite, and, since 3. is equivalent to a subspace of 3

:** (II.3.19), the dimension of 3 is finite. ... Q.E.D. From Corollary 7 it follows that

weak and strong convergence are the same in

from ...

Then the dimension of 3:** is finite, and, since 3. is equivalent to a subspace of 3

:** (II.3.19), the dimension of 3 is finite. ... Q.E.D. From Corollary 7 it follows that

weak and strong convergence are the same in

**finite dimensional**spaces andfrom ...

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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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