## Linear Operators, Part 1 |

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Page 419

Nelson Dunford, Jacob T. Schwartz. 2 DEFINITION . Let X be a linear vector

space , and let I be a total subspace of X * . Then the l '

[ ( 9 ) < € ...

Nelson Dunford, Jacob T. Schwartz. 2 DEFINITION . Let X be a linear vector

space , and let I be a total subspace of X * . Then the l '

**topology**of X is the**topology**obtained by taking as base all sets of the form N ( p ; A , 8 ) = { 9 ||| ( p ) -[ ( 9 ) < € ...

Page 420

Nelson Dunford, Jacob T. Schwartz. in the X *

weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of

y * , then each element y e Y determines the linear functional f , on X defined by 1

...

Nelson Dunford, Jacob T. Schwartz. in the X *

**topology**if and only if lim , xe = xweakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of

y * , then each element y e Y determines the linear functional f , on X defined by 1

...

Page 477

strong , and the weak operator

uniform operator

the strong operator

...

strong , and the weak operator

**topologies**in B ( X , Y ) . It is evident that theuniform operator

**topology**is stronger than the strong operator**topology**, and thatthe strong operator

**topology**is stronger than the weak operator**topology**. With its...

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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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