## Linear Operators: General theory |

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Page 254

Thus by forming the chain UB , UM , ... , Uz ' , Vz . it is

Thus by forming the chain UB , UM , ... , Uz ' , Vz . it is

**seen**that vp is equivalent to vg , and thus that Vp is in V. Since { vp } is a basis , the vector u , has an expansion of the form un = E ( ux , VB ) 0g , so that u , is in the ...Page 286

Since x * ( % ) converges , it is

Since x * ( % ) converges , it is

**seen**from the Vitali - HahnSaks theorem ( III.7.2 ) that lim S 8 ( s ) } , ( $ ) u ( ds ) = 0 uniformly in n . Since it is assumed for the present that u ( S ) < ooit is**seen**from Theorem III.6.15 that ...Page 715

Thus it is

Thus it is

**seen**from Theorem 5 that all the points of o ( T * ) of unit modulus are roots of unity , and by Lemma VII.3.7 the same holds for o ( T ) . The remaining conclusions in Theorems 6 and 7 are then provided exactly as before ...### 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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