## Linear Operators, Part 1 |

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Page 430

Our result now follows from Corollary 8 . Q.E.D. 6.

Compactness We have already introduced and employed the concepts of

sequential compactness ( II.3.25 ) and compactness in the X * ( or

topology .

Our result now follows from Corollary 8 . Q.E.D. 6.

**Weak**Topologies .**Weak**Compactness We have already introduced and employed the concepts of

**weak**sequential compactness ( II.3.25 ) and compactness in the X * ( or

**weak**)topology .

Page 477

strong , and the

uniform operator topology is stronger than the strong operator topology , and that

the strong operator topology is stronger than the

...

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 that

the strong operator topology is stronger than the

**weak**operator topology . With its...

Page 511

A set AC B ( X , Y ) is compact in the

closed in the

compact for each x € X. A set AC B ( X , Y ) is compact in the strong operator

topology if ...

A set AC B ( X , Y ) is compact in the

**weak**operator topology if and only if it isclosed in the

**weak**operator topology and the**weak**closure of Ax is weaklycompact for each x € X. A set AC B ( X , Y ) is compact in the strong operator

topology if ...

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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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