Linear Operators: General theory |
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Page 415
Hence ko e p - A , and thus p e A + k , CA + K . Q.E.D. Since the commutativity of
the group G is not essential to the proof , the same result holds for non - Abelian
topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X : ( i ) co
...
Hence ko e p - A , and thus p e A + k , CA + K . Q.E.D. Since the commutativity of
the group G is not essential to the proof , the same result holds for non - Abelian
topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X : ( i ) co
...
Page 434
and proceed as in the first part of the proof of the preceding theorem to construct
a subsequence { ym } of { Xn } such that limm - * x * ym exists for each x * in the
set H of that proof . Let Km = co { ym , Ym + ] , . . . } and let yo be an arbitrary point
...
and proceed as in the first part of the proof of the preceding theorem to construct
a subsequence { ym } of { Xn } such that limm - * x * ym exists for each x * in the
set H of that proof . Let Km = co { ym , Ym + ] , . . . } and let yo be an arbitrary point
...
Page 699
The proof of this lemma is the most involved of all the steps in the proof of Lemma
11 as outlined in the diagram : C → CPk DPx = Dx → Cx . The proof of the
implication CP DPk which is the proof of Lemma 14 is very similar to the proof of
the ...
The proof of this lemma is the most involved of all the steps in the proof of Lemma
11 as outlined in the diagram : C → CPk DPx = Dx → Cx . The proof of the
implication CP DPk which is the proof of Lemma 14 is very similar to the proof of
the ...
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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 |