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Page 462
116 ] . Dieudonné [ 3 ; p . 109 ] proved 3 . 9 after establishing Lemma 3 . 10 by
induction . The case of Theorem 3 . 9 in which X = Y * and I ' = Y , was proved in
the separable case by Banach [ 1 ; p . 131 ] and in full generality by Alaoglu 1 ; p .
116 ] . Dieudonné [ 3 ; p . 109 ] proved 3 . 9 after establishing Lemma 3 . 10 by
induction . The case of Theorem 3 . 9 in which X = Y * and I ' = Y , was proved in
the separable case by Banach [ 1 ; p . 131 ] and in full generality by Alaoglu 1 ; p .
Page 802
The singular elements of a Banach algebra . Duke Math . J . 14 , 1063 - 1077 (
1947 ) . 5 . Isomorphic groups of linear transformations . Amer . J . Math . 72 , 451
- 464 ( 1950 ) . 6 . Banach algebras with an adjoint operation . Ann . of Math .
The singular elements of a Banach algebra . Duke Math . J . 14 , 1063 - 1077 (
1947 ) . 5 . Isomorphic groups of linear transformations . Amer . J . Math . 72 , 451
- 464 ( 1950 ) . 6 . Banach algebras with an adjoint operation . Ann . of Math .
Page 804
On a class of Markoff processes . Trans . Amer . Math . Soc . 71 , 120 - 135 ( 1951
) . Rosenbloom , P . C . 1 . Elements of mathematical logic . Dover Publications ,
New York , 1950 . 2 . Perturbations of linear operators in Banach spaces .
On a class of Markoff processes . Trans . Amer . Math . Soc . 71 , 120 - 135 ( 1951
) . Rosenbloom , P . C . 1 . Elements of mathematical logic . Dover Publications ,
New York , 1950 . 2 . Perturbations of linear operators in Banach spaces .
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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 |