## Linear Operators: General theory |

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Page 245

Every linear operator on a

Every linear operator 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 that every x in X has a unique representation in the ...Page 246

Then the dimension of X ** is

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**. Hence , from the first part of this proof , X and X * have the same dimension .Page 290

It is obvious that \ w * ) = [ gc , and so fæ * 1 = ' glcNow suppose that ( S , E , u ) is o -

It is obvious that \ w * ) = [ gc , and so fæ * 1 = ' glcNow suppose that ( S , E , u ) is o -

**finite**, and let En be an increasing sequence of measurable sets of**finite**measure whose union is S. Using the theorem for L ( En ) = L ( En ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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