## Linear Operators: General theory |

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Page 54

Since the

Since the

**mapping**x = x / k , is a homeomorphism of X with itself , by 10 ( ii ) , 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**mapping**of one F ...Page 493

Conversely , if ( a ) and ( b ) are satisfied for the

Conversely , if ( a ) and ( b ) are satisfied for the

**mapping**which sends x * into u ( • ) ** , then it follows that for each fixed f e C ( S ) the**mapping**** > st ( s ) u ( ds ) ** is continuous in the X topology of X * and therefore ...Page 513

12 If H is a Hilbert space , the

12 If H is a Hilbert space , the

**mapping**T → T * of B ( v ) into itself is continuous with either the uniform or weak operator topology . By considering the sequence { An } defined in Exercise 11 , show that this**mapping**is not ...### 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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