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Products and Direct Sums in Locally Convex Cones

Published online by Cambridge University Press:  20 November 2018

M. R. Motallebi  and
H. Saiflu
M. R. Motallebi
Affiliation:
Department of Mathematics, University of Mohaghegh Ardabili, P. O. Box 179, Ardabil, Irane-mail: motallebi@uma.ac.ir
H. Saiflu
Affiliation:
Department of Mathematics, Tabriz University, Tabriz, Irane-mail: saiflu@tabrizu.ac.ir
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Abstract

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In this paper we define lower, upper, and symmetric completeness and discuss closure of the sets in products and direct sums. In particular, we introduce suitable bases for these topologies, which leads us to investigate completeness of the direct sum and its components. Some results obtained about $X$-topologies and polars of the neighborhoods.

Keywords

20K2546A3046A20product and direct sumdualitylocally convex cone
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 783 - 798
Copyright
Copyright © Canadian Mathematical Society 2012

References

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[3] Ranjbari, A. and Saiflu, H., Projective and inductive limits in locally convex cones. J. Math. Anal. Appl. 332(2007), 1097–1108. http://dx.doi.org/10.1016/j.jmaa.2006.11.001 Google Scholar
[4] Roth, W., A uniform boundedness theorem for locally convex cones. Proc. Amer. Math. Soc. 126(1998), 1973–1982. http://dx.doi.org/10.1090/S0002-9939-98-04699-1 Google Scholar