## Linear Operators, Part 1 |

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Page 245

An n -

operator on a finite

b1 , ... , bn } be a Hamel basis for the finite

...

An n -

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

**dimensional**normed linear space is continuous . Proof . Let {b1 , ... , 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 X** ( 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 .Page 556

Spectral Theory in a Finite

denote a finite

Our aim is to study the algebraic and topological properties of T. This is achieved

...

Spectral Theory in a Finite

**Dimensional**Space Throughout this section , X willdenote a finite

**dimensional**complex B - space , and T a linear operator in B ( X ) .Our aim is to study the algebraic and topological properties of T. This is achieved

...

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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

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