## Linear Operators, Part 1 |

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Page 22

This contradiction proves that A is

that A is

. Let po be an arbitrary point of A, and let do = sup 9(po, p). The number do is

finite ...

This contradiction proves that A is

**sequentially compact**. Conversely, supposethat A is

**sequentially compact**and closed. It will first be shown that A is separable. Let po be an arbitrary point of A, and let do = sup 9(po, p). The number do is

finite ...

Page 314

Q.E.D. 12 THEOREM. A subset K of bass, 2) is weakly

and only if there exists a non-negative u in bass, 2) such that lim Å(E) = 0 a(E)—-

0 uniformly for Že K. PRoof. Let K C bass, 2) be weakly

...

Q.E.D. 12 THEOREM. A subset K of bass, 2) is weakly

**sequentially compact**ifand only if there exists a non-negative u in bass, 2) such that lim Å(E) = 0 a(E)—-

0 uniformly for Že K. PRoof. Let K C bass, 2) be weakly

**sequentially compact**and...

Page 511

Then if A is compact in the weak operator topology, so is the weak operator

closure of co(A). If A is compact in the strong operator topology, so is the strong

operator closure of co(A). 4 If a set A C B(3, 3)) is

weak ...

Then if A is compact in the weak operator topology, so is the weak operator

closure of co(A). If A is compact in the strong operator topology, so is the strong

operator closure of co(A). 4 If a set A C B(3, 3)) is

**sequentially compact**in theweak ...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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