Linear Operators: General theory |
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Page 68
The space X is said to be weakly complete if every weak Cauchy sequence has a
weak limit . In Chapter V , a topology is introduced in certain linear spaces in
such a way that they become Hausdorff spaces in which the notion of
convergence ...
The space X is said to be weakly complete if every weak Cauchy sequence has a
weak limit . In Chapter V , a topology is introduced in certain linear spaces in
such a way that they become Hausdorff spaces in which the notion of
convergence ...
Page 127
It is evident that such a sequence has the limit Un , En . A non - increasing
sequence { En } is one for which En2 En + 1 , n = 1 , 2 , . . . . Such a sequence has
the limit n i En . A monotone sequence is one which is either non - decreasing or
non ...
It is evident that such a sequence has the limit Un , En . A non - increasing
sequence { En } is one for which En2 En + 1 , n = 1 , 2 , . . . . Such a sequence has
the limit n i En . A monotone sequence is one which is either non - decreasing or
non ...
Page 658
Thus , from the physical point of view , the time T involved in the experiment is
large enough to give a good value for the limit ( iii ) lim = f ( de ( cc ) ) dt , T + 00
TJO which , in physical theories , is assumed to exist . Thus , the mathematician is
...
Thus , from the physical point of view , the time T involved in the experiment is
large enough to give a good value for the limit ( iii ) lim = f ( de ( cc ) ) dt , T + 00
TJO which , in physical theories , is assumed to exist . Thus , the mathematician is
...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
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Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Volume 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics |
| Author | Nelson Dunford |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |