## Linear Operators, Part 1 |

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Page 495

Since B , is an algebra and

- field contained in B. We now show that B. = B by proving that B contains all the

closed sets . Let F be an arbitrary closed set in S. Since S is assumed to be a ...

Since B , is an algebra and

**satisfies**condition ( ii ) , it is readily seen that B , is a o- field contained in B. We now show that B. = B by proving that B contains all the

closed sets . Let F be an arbitrary closed set in S. Since S is assumed to be a ...

Page 498

on to X *

norm

countably additive on in the strong topology of X * . Proof . If , for E in E , the

functional x ...

on to X *

**satisfies**( i ) then ( ii ) defines an operator T on X to L ( S , E , ” ) whosenorm

**satisfies**( iii ) . Furthermore T is weakly compact if and only if x * ( ) iscountably additive on in the strong topology of X * . Proof . If , for E in E , the

functional x ...

Page 557

Consequently , the product R , of all the factors ( 2–2 ; ) " in R such that li € ( T ) ,

still

divisible by R . ,, any such polynomial

...

Consequently , the product R , of all the factors ( 2–2 ; ) " in R such that li € ( T ) ,

still

**satisfies**R ( T ) = 0. In the same way , the ... order via ) at each i.co ( T ) isdivisible by R . ,, any such polynomial

**satisfies**P ( T ) = 0 . To prove the converse...

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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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