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|標題:||On sigma-limit and s sigma-limit in Banach spaces||作者:||Li, S.
|關鍵字:||Banach limit;weak almost convergence;strong almost convergence;sigma-limit;s sigma-limit;Bochner integrable;Lebesgue dominated;convergence theorem;invariant means||Project:||Taiwanese Journal of Mathematics||期刊/報告no：:||Taiwanese Journal of Mathematics, Volume 9, Issue 3, Page(s) 359-371.||摘要:||
For bounded sequences in a normed linear space X, we introduce a notion of limit, called the s sigma-limit, and discuss some interesting properties related to sigma-limit and s sigma-limit. It is shown that the space X-s sigma (resp. X-sigma) of all s sigma-convergent (resp. sigma-convergent) sequences in X is a Banach space, and the space C-s sigma is a unital Banach subalgebra, of l(infinity) such that every Banach limit restricted to C-s sigma is a multiplicative linear functional. We also use s sigma-limit to characterize continuity of functions and prove two versions of the dominated convergence theorem in terms of sigma-limit and s sigma-limit.
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