## Linear Operators: General theory |

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Page 495

Since B , is an algebra and

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 ...Page 498

on to X *

on to X *

**satisfies**( i ) then ( ii ) defines an operator T on X to L ( S , E , ” ) whose norm**satisfies**( iii ) . Furthermore T is weakly compact if and only if x * ( ) is countably additive on in the strong topology of X * . Proof .Page 557

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

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 product R , of all the factors ( 2--2 ; ) , where Bi = min ...### 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 | |

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