Linear Operators, Part 1 |
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Page 67
A closed linear manifold in a reflexive B - space is reflerive . Proof . Let y be a
closed linear manifold in the reflexive space X. Let 5 : x * y * be defined by the
equation $ ( x * ) y = x * y , y e Y. Clearly 15 ( x * ) = \ * , so that $ : X * → Y * . Let n
: y ...
A closed linear manifold in a reflexive B - space is reflerive . Proof . Let y be a
closed linear manifold in the reflexive space X. Let 5 : x * y * be defined by the
equation $ ( x * ) y = x * y , y e Y. Clearly 15 ( x * ) = \ * , so that $ : X * → Y * . Let n
: y ...
Page 72
I 19 If X is a reflexive B - space , and 3 is a closed subspace of X , show , using
Exercise 18 , that both 3 and X / 3 are reflexive . 220 If X is a B - space , with 3CX
, and both 3 and X 3 are reflexive , then X is reflexive . ( Hint : Given any *** e X **
...
I 19 If X is a reflexive B - space , and 3 is a closed subspace of X , show , using
Exercise 18 , that both 3 and X / 3 are reflexive . 220 If X is a B - space , with 3CX
, and both 3 and X 3 are reflexive , then X is reflexive . ( Hint : Given any *** e X **
...
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 .
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |