## Linear Operators: General theory |

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Page 419

Then the l '

form N ( p ; A , ε ) = { 9 | | | ( p ) - | ( 9 ) < E , 7 € A } , where pe X , A is a finite subset

of P , and a > 0 . The terms I ' - open and I - closed subsets of X , I - continuous ...

Then the l '

**topology**of X is the**topology**obtained by taking as base all sets of theform N ( p ; A , ε ) = { 9 | | | ( p ) - | ( 9 ) < E , 7 € A } , where pe X , A is a finite subset

of P , and a > 0 . The terms I ' - open and I - closed subsets of X , I - continuous ...

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

...

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

**topology**if and only if lim , Xx = xweakly in the sense of Definition II . 3 . 25 . On the other hand , if X is a subspace

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

...

Page 512

is compact in the strong operator

sequentially compact in the weak operator

the weak operator

X , Y ) is ...

is compact in the strong operator

**topology**. If Y is also separable , A issequentially compact in the weak operator

**topology**if and only if A is compact inthe weak operator

**topology**. 6 If Y is reflexive , then the closed unit sphere of B (X , Y ) is ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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