## Linear Operators: General theory |

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Page xvi

The set A is said to be a proper subset of the set B if A C B and A + B . The

notation ACB , or B A , will

of a set A relative to a set B is the set whose elements are in B but not in A , i . e . ,

the ...

The set A is said to be a proper subset of the set B if A C B and A + B . The

notation ACB , or B A , will

**mean**that A is a proper subset of B . The complementof a set A relative to a set B is the set whose elements are in B but not in A , i . e . ,

the ...

Page 261

The space rba ( S ) is partially ordered by defining u 22 to

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

) is partially ordered by defining 1 3g to

The space rba ( S ) is partially ordered by defining u 22 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 1 3g 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 ...

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 ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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