Linear Operators: General theory |
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Page 67
A closed linear manifold in a reflexive B - space is reflexive . Proof . Let y be a
closed linear manifold in the reflexive space X. Let 5 : x * → y * be defined by the
equation ( ** ) y = x * y , y e Y. Clearly $ ( x * ) = 2 * , so that $ : X * → Y * . Let n : y
...
A closed linear manifold in a reflexive B - space is reflexive . Proof . Let y be a
closed linear manifold in the reflexive space X. Let 5 : x * → y * be defined by the
equation ( ** ) y = x * y , y e Y. Clearly $ ( x * ) = 2 * , so that $ : X * → Y * . Let n : y
...
Page 88
Reflexivity . The fact that the natural isomorphism of a B - space X into its second
conjugate is isometric was proved by Hahn [ 3 ; p . 219 ] who was ... He used the
term regular to describe what we , following Lorch [ 2 ] , have called reflexive .
Reflexivity . The fact that the natural isomorphism of a B - space X into its second
conjugate is isometric was proved by Hahn [ 3 ; p . 219 ] who was ... He used the
term regular to describe what we , following Lorch [ 2 ] , have called reflexive .
Page 425
A B - space is reflexive if and only if its closed unit sphere is compact in the weak
topology . PROOF . Let X be a reflexive B - space , and let z be the natural
embedding of X onto X ** . Then x and x - 1 are isometries , and x maps the
closed unit ...
A B - space is reflexive if and only if its closed unit sphere is compact in the weak
topology . PROOF . Let X be a reflexive B - space , and let z be the natural
embedding of X onto X ** . Then x and x - 1 are isometries , and x maps the
closed unit ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
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Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1; Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |