## Linear Operators: General theory |

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Page 54

Since the

proof is complete . Q.E.D. We now are in a position to prove a number of basic

results about F - spaces . 14 THEOREM . A linear

Since the

**mapping**x = x / k , is a homeomorphism of X with itself , by 10 ( ii ) , theproof is complete . Q.E.D. We now are in a position to prove a number of basic

results about F - spaces . 14 THEOREM . A linear

**mapping**of one F - space into ...Page 455

In this case , the

continuous

which contains at least two points . Consider the

since G is ...

In this case , the

**mapping**H : K → lz , defined by H ( k ) = [ gi ( k ) ] , is acontinuous

**mapping**of K onto a compact convex subset K , of the Hilbert cubewhich contains at least two points . Consider the

**mapping**To = HTI - 1 : K , → Ko ;since G is ...

Page 525

11 valued u - measurable functions defined on S. Let T be a linear

into M. If T is a bounded linear

of this operator , otherwise let T , +00 . Then log T 1 / a is a convex function of a ...

11 valued u - measurable functions defined on S. Let T be a linear

**mapping**of Xinto M. If T is a bounded linear

**mapping**of X into L ( S , E , u ) , let T , be the normof this operator , otherwise let T , +00 . Then log T 1 / a is a convex function of a ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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