## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 82

Page 430

employed the concepts of

compactness in the X * ( or

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

**weak**sequential compactness ( II . 3 . 25 ) andcompactness in the X * ( or

**weak**) topology . There is at least one other type of**weak**...Page 511

2 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 ...

2 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 ...

Page 858

9 ( 7 ) Wiener measure space , ( 405 )

67 ) properties , II . 3 . 26 – 27 ( 68 ) in special spaces , IV . 15

additivity , definition , ( 318 ) and strong , IV . 10 . 1 ( 318 )

II .

9 ( 7 ) Wiener measure space , ( 405 )

**Weak**convergence , definition , II . 3 . 25 (67 ) properties , II . 3 . 26 – 27 ( 68 ) in special spaces , IV . 15

**Weak**countableadditivity , definition , ( 318 ) and strong , IV . 10 . 1 ( 318 )

**Weak**limit , definition ,II .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero