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A note on product topologies in locally convex cones | ||
| Journal of Mahani Mathematical Research | ||
| دوره 11، شماره 1 - شماره پیاپی 21، فروردین 2022، صفحه 61-67 اصل مقاله (442.43 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.18239.1170 | ||
| نویسنده | ||
| Mohammad Reza Motallebi* | ||
| University of Mohaghegh Ardabili, Ardabil, Iran. | ||
| چکیده | ||
| We consider the locally convex product cone topologies and prove that the product topology of weakly cone-complete locally convex cones is weakly cone-complete. In particular, we deduce that a product cone topology is barreled whenever its components are weakly cone-complete and carry the countable neighborhood bases. | ||
| کلیدواژه‌ها | ||
| Products cone topologies؛ weak cone-completeness؛ barreledness | ||
| مراجع | ||
|
1] K. Keimel, W. Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer Verlag, Heidelberg-Berlin-New York, 1992.
[2] M.R. Motallebi, Locally convex product and direct sum cones, Mediterr. J. Math., 11 3 (2014), 913-927
[3] M.R. Motallebi, On weak completeness of products and direct sums in locally convex cones, Period. Math. Hung., 75 2(2017), 322-329
[4] M.R. Motallebi, Weak compactness in locally convex cones, Positivity, 23 2(2019), 303-313
[5] M.R. Motallebi, Weak compactness of direct sums in locally convex cones, Stud. Sci. Math. Hung., 55 4(2018), 487-497
[6] M.R. Motallebi, H. Saiu, Products and direct sums in locally convex cones, Can. Math. Bull. vol. 55 4, (2012), 783-798.
[7] W. Roth, A uniform boundedness theorem for locally convex cones, Proc. Amer. Math. Soc. 126 7(1998), 1973-1982
[8] W. Roth, Locally convex lattice cones, J. Convex Anal. 16 (1), (2009), 1-31. | ||
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