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Page 419
Nelson Dunford, Jacob T. Schwartz, William G. Bade. 2 DEFINITION . Let X be a
linear vector space , and let I be a total subspace of X * . Then the I topology of X
is the topology obtained by taking as base all sets of the form N ( p ; A , ε ) = { 9 ...
Nelson Dunford, Jacob T. Schwartz, William G. Bade. 2 DEFINITION . Let X be a
linear vector space , and let I be a total subspace of X * . Then the I topology of X
is the topology obtained by taking as base all sets of the form N ( p ; A , ε ) = { 9 ...
Page 420
Nelson Dunford, Jacob T. Schwartz, William G. Bade. in the X * topology if and
only if lim , Xx = x weakly in the sense of Definition II . 3 . 25 . On the other hand ,
if X is a subspace of yî , then each element y e Y determines the linear functional f
...
Nelson Dunford, Jacob T. Schwartz, William G. Bade. in the X * topology if and
only if lim , Xx = x weakly in the sense of Definition II . 3 . 25 . On the other hand ,
if X is a subspace of yî , then each element y e Y determines the linear functional f
...
Page 512
is compact in the strong operator topology . If Y is also separable , A is
sequentially compact in the weak operator topology if and only if A is compact in
the weak operator topology . 6 If Y is reflexive , then the closed unit sphere of B (
X , Y ) is ...
is compact in the strong operator topology . If Y is also separable , A is
sequentially compact in the weak operator topology if and only if A is compact in
the weak operator topology . 6 If Y is reflexive , then the closed unit sphere of B (
X , Y ) is ...
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Contents
Metric Spaces | 19 |
Convergence and Uniform Convergence of Generalized | 26 |
Exercises | 33 |
Copyright | |
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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak 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 |