## Linear Operators, Part 1 |

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Page 287

Thus ( 0 * = \ gle The mapping x * → g is then a one - to - one isometric map of L *

into Lg . It is

L * satisfying ( i ) , so that the mapping x * * → g is a one - to - one isometric ...

Thus ( 0 * = \ gle The mapping x * → g is then a one - to - one isometric map of L *

into Lg . It is

**evident**from the Hölder inequality that any g € L , determines an x * €L * satisfying ( i ) , so that the mapping x * * → g is a one - to - one isometric ...

Page 299

... it follows that all the functions G1 , ... , & y vanish outside some sufficiently large

interval [ -A0 , +4 . ] , so that s + S | ) Pdy = $ + S- * My ) –s : ( y ) pdy Sly - g ; ” SEP

for A 2 A0 , proving ( b ) . To prove ( a ) we note first that it is

... it follows that all the functions G1 , ... , & y vanish outside some sufficiently large

interval [ -A0 , +4 . ] , so that s + S | ) Pdy = $ + S- * My ) –s : ( y ) pdy Sly - g ; ” SEP

for A 2 A0 , proving ( b ) . To prove ( a ) we note first that it is

**evident**that lim ...Page 337

It is then

isomorphic with the closed subspace BV ( 1 ) of all | e BV ( 1 ) such that f ( a + ) =

0 . If N is the one - dimensional space of constant functions , it is

I ) ...

It is then

**evident**that v ( us , I ) = v ( 1 , 1 ) . Thus , ba ( S , E ) is isometricallyisomorphic with the closed subspace BV ( 1 ) of all | e BV ( 1 ) such that f ( a + ) =

0 . If N is the one - dimensional space of constant functions , it is

**evident**that BV (I ) ...

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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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