Linear Operators: General theory |
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Page 45
Expressed differently , the cofactor of aig is obtained by replacing the element Aig
and all the other elements of the ith row and jth column by 0 and calculating the
resulting determinant . Denoting the cofactor of aig by Aij , it may be seen that by
...
Expressed differently , the cofactor of aig is obtained by replacing the element Aig
and all the other elements of the ith row and jth column by 0 and calculating the
resulting determinant . Denoting the cofactor of aig by Aij , it may be seen that by
...
Page 387
among other things , that the Bohr compactification of a locally compact Abelian
group G may be obtained by taking the character group Ĝ of G , equipping Ĝ with
its discrete topology , and then taking the character group of this discrete group .
among other things , that the Bohr compactification of a locally compact Abelian
group G may be obtained by taking the character group Ĝ of G , equipping Ĝ with
its discrete topology , and then taking the character group of this discrete group .
Page 607
54 , 2 ] had obtained expansions for the resolvent ( 21 - T ) - 1 in the
neighborhood of a pole . A special case of Theorem 1 . 9 is due to Weyr [ 1 ] , and
in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1 . 10 ,
Frobenius [ 3 ; p .
54 , 2 ] had obtained expansions for the resolvent ( 21 - T ) - 1 in the
neighborhood of a pole . A special case of Theorem 1 . 9 is due to Weyr [ 1 ] , and
in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1 . 10 ,
Frobenius [ 3 ; p .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Common terms and phrases
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 |