## Linear Operators, Part 1 |

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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 493

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

• ) ** , then it follows that for each fixed f e C ( S ) the

** is continuous in the X topology of X * and therefore ( V.3.9 ) is generated by ...

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 ( V.3.9 ) is generated by ...

Page 513

12 If H is a Hilbert space , the

with either the uniform or weak operator topology . By considering the sequence {

An } defined in Exercise 11 , show that this

12 If H is a Hilbert space , the

**mapping**T → T * of B ( v ) into itself is continuouswith either the uniform or weak operator topology . By considering the sequence {

An } defined in Exercise 11 , show that this

**mapping**is not continuous in the ...### 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 | |

87 other sections not shown

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