## Linear Operators: General theory |

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Page 245

Every linear operator on a

PROOF . Let { b1 , ... , bn } be a Hamel basis for the

linear space X so that every x in X has a unique representation in the form x = a

bit ...

Every linear operator on a

**finite**dimensional normed linear space is continuous .PROOF . Let { b1 , ... , bn } be a Hamel basis for the

**finite**dimensional normedlinear space X so that every x in X has a unique representation in the form x = a

bit ...

Page 290

Now suppose that ( S , E , u ) is o -

of measurable sets of

En ) = L ( En , E ( En ) , k ) , we obtain a sequence { gn } of functions in Lo such ...

Now suppose that ( S , E , u ) is o -

**finite**, and let E , be an increasing sequenceof measurable sets of

**finite**measure whose union is S. Using the theorem for L (En ) = L ( En , E ( En ) , k ) , we obtain a sequence { gn } of functions in Lo such ...

Page 849

( See Decomposition ) definition , III.4.3 ( 126 )

extension of , 111.5.18 ( 143 ) a metric space , I11.7.1 ( 158 ) , as measure in a

group , ( 90-91 ) topology in. normal , VII.2.14 ( 563 ) of a projection , VI.9.27 ( 514

) ...

( See Decomposition ) definition , III.4.3 ( 126 )

**finite**, III.4.3 ( 126 ) Lebesgueextension of , 111.5.18 ( 143 ) a metric space , I11.7.1 ( 158 ) , as measure in a

group , ( 90-91 ) topology in. normal , VII.2.14 ( 563 ) of a projection , VI.9.27 ( 514

) ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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