## Linear Operators: General theory |

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Results 1-3 of 4

Page 435

13 , it follows from Theorem 1 that it suffices to show that co ( A ) is weakly

sequentially compact . Let { Pn } be a sequence of points in co ( A ) ; then pn is a

convex combina

sp ( B ...

13 , it follows from Theorem 1 that it suffices to show that co ( A ) is weakly

sequentially compact . Let { Pn } be a sequence of points in co ( A ) ; then pn is a

convex combina

**tion**of a finite set Bn of points of A . Let Bo = U - Bn , and let Xo =sp ( B ...

Page 657

mechanics of Gibbs and Boltzmann concerns the existence of certain types of

time averages . The problem may be formulated in abstract terms as follows : The

...

**tion**y 4. Ergodic Theory A fundamental mathematical question in the statisticalmechanics of Gibbs and Boltzmann concerns the existence of certain types of

time averages . The problem may be formulated in abstract terms as follows : The

...

Page

Nelson Dunford, Jacob T. Schwartz. a certain 4 aation tiga 7 for

UNIVERSITY OF MICHIGAN 3 9015 02654 6591.

Nelson Dunford, Jacob T. Schwartz. a certain 4 aation tiga 7 for

**tion**, I .UNIVERSITY OF MICHIGAN 3 9015 02654 6591.

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero