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Cited by 8 publications
(2 citation statements)
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“…Then F = Z G y is in A Since T,N 0 (Gj) < oo. Also oj As e > 0 was arbitrary, AT(F (1) + F (2) ) ^ N(F (1) )+N(F (2) ), which concludes the proof (ii) In establishing (ii) we will use the fact that a normed linear space is complete if and only if every absolutely summable series is summable. So let {F (l) } be an absolutely summable series in (A, N).…”
Section: J 00 J \F(uu--t* N )\Qxp^ -[U Lmentioning
confidence: 77%
“…Then F = Z G y is in A Since T,N 0 (Gj) < oo. Also oj As e > 0 was arbitrary, AT(F (1) + F (2) ) ^ N(F (1) )+N(F (2) ), which concludes the proof (ii) In establishing (ii) we will use the fact that a normed linear space is complete if and only if every absolutely summable series is summable. So let {F (l) } be an absolutely summable series in (A, N).…”
Section: J 00 J \F(uu--t* N )\Qxp^ -[U Lmentioning
confidence: 77%
“…We are now ready to state and prove the main two theorems of this section. (i) Let F (1) and F {2) be elements of A. Let e > 0 be given.…”
Section: J 00 J \F(uu--t* N )\Qxp^ -[U Lmentioning
confidence: 99%
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