Linear Operators, Part 1 |
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Page 169
5 Show that ( i ) , ( ii ) , and ( iii ) of Theorem 3.6 imply that f is in L , ( S , E , \ ) and
that in - f , converges to zero even if { / n } is a generalized sequence . 6 Let u be
bounded . Suppose that the field Eis separable under the metric g ( E , F ) = v ( u
...
5 Show that ( i ) , ( ii ) , and ( iii ) of Theorem 3.6 imply that f is in L , ( S , E , \ ) and
that in - f , converges to zero even if { / n } is a generalized sequence . 6 Let u be
bounded . Suppose that the field Eis separable under the metric g ( E , F ) = v ( u
...
Page 204
a , ( ds ) does not converge to zero and since 0 < In ( sa ) si it follows from the
dominated convergence theorem ( 6.16 ) that there is a point in Sa for which In (
sq ) is defined for all n and for which the sequence { fn ( $ & ) } does not converge
to ...
a , ( ds ) does not converge to zero and since 0 < In ( sa ) si it follows from the
dominated convergence theorem ( 6.16 ) that there is a point in Sa for which In (
sq ) is defined for all n and for which the sequence { fn ( $ & ) } does not converge
to ...
Page 557
In the same way , there exist non - zero polynomials Si , i = 2 , ... , k such that S ( T
) x ; = 0 . If R = S : S ... Sx , then R ( T ) x ; = 0 , and consequently R ( T ) x = 0 for
all x e X. Thus a non - zero polynomial R exists such that R ( T ) Let R be factored
...
In the same way , there exist non - zero polynomials Si , i = 2 , ... , k such that S ( T
) x ; = 0 . If R = S : S ... Sx , then R ( T ) x ; = 0 , and consequently R ( T ) x = 0 for
all x e X. Thus a non - zero polynomial R exists such that R ( T ) Let R be factored
...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
87 other sections not shown
Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |