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Almost Convergence of Sequences in Banach Spaces in Weak, Strong, and Absolute Senses
| Content Provider | Semantic Scholar |
|---|---|
| Author | Li, Yuan-Chuan |
| Copyright Year | 2006 |
| Abstract | We introduce concepts of σ-lim sup and σ-lim inf for bounded sequences of real numbers and show a Cauchy criterion for sequences of vectors which converge in the sense of aσ-limit (i.e., absolute almost convergence). Then a sufficient condition on a bounded sequence {{x(m) n }∞ n=1 }∞ m=1 ⊂ ∞(X) is given for the following equality to hold: aσ- lim m→∞σ- lim n→∞x(m) n = σ- lim n→∞aσ- lim m→∞x(m) n . Finally, applying this result we show that σ- lim n→∞ f(sin(nθ)) and σ- lim n→∞ f(cos(nθ)) exist whenever f is a weakly continuous function on [−1, 1] with values in a reflexive Banach space. |
| Starting Page | 209 |
| Ending Page | 218 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.11650/tjm.10.2006.881 |
| Volume Number | 10 |
| Alternate Webpage(s) | http://journal.taiwanmathsoc.org.tw/~journal/tjm/V10N1/0601_18.pdf |
| Alternate Webpage(s) | https://doi.org/10.11650/tjm.10.2006.881 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
