## Linear Operators, Part 1 |

### From inside the book

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Page 430

Q.E.D. 6.

and employed the concepts of

compactness in the X * ( or

Q.E.D. 6.

**Weak**Topologies .**Weak**Compactness 1 We have already introducedand employed 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 512

If Y is also separable , A is sequentially compact in the

and only if A is compact in the

the closed unit sphere of B ( X , Y ) is compact in the

If Y is also separable , A is sequentially compact in the

**weak**operator topology ifand only if A is compact in the

**weak**operator topology . 6 If Y is reflexive , thenthe closed unit sphere of B ( X , Y ) is compact in the

**weak**operator topology .Page 858

... definition , I.2.8 ( 7 ) well - ordering theorem , I.2.9 ( 7 ) Wiener measure space ,

( 405 )

special spaces , IV.15

... definition , I.2.8 ( 7 ) well - ordering theorem , I.2.9 ( 7 ) Wiener measure space ,

( 405 )

**Weak**convergence , definition , II.3.25 ( 67 ) properties , II.3.26–27 ( 68 ) inspecial spaces , IV.15

**Weak**countable additivity , definition , ( 318 ) and strong ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 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

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 isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space 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