## Linear Operators, Part 1 |

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Results 1-3 of 72

Page 261

The space rba ( S ) is partially ordered by defining u 2 i to

) for every E in the field determined by the closed sets . Similarly , the space C ( S

) is partially ordered by defining i 2 g to

The space rba ( S ) is partially ordered by defining u 2 i to

**mean**that u ( E ) 2 2 ( E) for every E in the field determined by the closed sets . Similarly , the space C ( S

) is partially ordered by defining i 2 g to

**mean**that f ( s ) g ( s ) for all s in S.Page 660

These results are applied to obtain , in Section 7 , corresponding

pointwise convergence theorems for the continuous case . Section 8 is

concerned with a certain class of operators T for which the sequence of averages

{ N - 1 EN = 1 ...

These results are applied to obtain , in Section 7 , corresponding

**mean**andpointwise convergence theorems for the continuous case . Section 8 is

concerned with a certain class of operators T for which the sequence of averages

{ N - 1 EN = 1 ...

Page 724

33 ( Dunford - Miller ) Let S , E , m , 4 , be as in Exercise 31. Show that limn70n -

1 { = 0 } ( qis ) converges in the

only if there exists a constant K < 00 such that 1 n - 1 - m ( - ie ) Km ( e ) ...

33 ( Dunford - Miller ) Let S , E , m , 4 , be as in Exercise 31. Show that limn70n -

1 { = 0 } ( qis ) converges in the

**mean**of L ( S , E , m ) for every 1 L ( S , E , m )only if there exists a constant K < 00 such that 1 n - 1 - m ( - ie ) Km ( e ) ...

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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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