## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 61

Page 12

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. listed in

Lemma 5 , so that the family of complements of elements of F is a topology . The

set Ā is the

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. listed in

Lemma 5 , so that the family of complements of elements of F is a topology . The

set Ā is the

**closure**of A in this topology . PROOF . Statements 10 ( b ) , ( d ) show...

Page 432

To see this , let m be an arbitrary integer ; since x ** is in the X * -

, there is an element zm € A such that 2 * ( cm ) - ** ( * ) < 1m , i 1 , ... , n . Since A

is weakly sequentially compact , a subsequence of { zm } will converge weakly ...

To see this , let m be an arbitrary integer ; since x ** is in the X * -

**closure**of x ( A ), there is an element zm € A such that 2 * ( cm ) - ** ( * ) < 1m , i 1 , ... , n . Since A

is weakly sequentially compact , a subsequence of { zm } will converge weakly ...

Page 511

A set AC B ( X , Y ) is compact in the weak operator topology if and only if it is

closed in the weak operator topology and the weak

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 is

closed 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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