Open Access

# Comment on 'A uniform boundedness theorem for locally convex cones' [W. Roth, Proc. Amer. Math. Soc. 126 (1998), 1973-1982]

### Abstract

In page 1975 of [W. Roth, A uniform boundedness theorem for locally convex cones, Proc. Amer. Math. Soc. 126 (1998), no.7, 1973-1982] we can see: In a locally convex vector space $E$ a barrel is defined to be an absolutely convex closed and absorbing subset $A$ of $E$. The set $U = \{(a,b)\in E^2,\ a-b\in A\}$ then is seen to be a barrel in the sense of Roth's definition. With a counterexample, we show that it is not enough for $U$ to be a barrel in the sense of Roth's definition. Then we correct this error with providing its converse and an application.

Key words: Locally convex cone, barrel.

### Article Information

 Title Comment on 'A uniform boundedness theorem for locally convex cones' [W. Roth, Proc. Amer. Math. Soc. 126 (1998), 1973-1982] Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 3, 292-295 MathSciNet MR3242710 zbMATH 1324.46017 Milestones Received 02/06/2013 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

Davod Saeedi
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.

Ismail Nikoufar
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.

Husain Saiflu
Department of Pure Mathematics, Faculty of Mathematical Sciences, Tabriz University, Tabriz, Iran. 02/06/2013

### Citation Example

Davod Saeedi, Ismail Nikoufar, and Husain Saiflu, Comment on 'A uniform boundedness theorem for locally convex cones' [W. Roth, Proc. Amer. Math. Soc. 126 (1998), 1973-1982], Methods Funct. Anal. Topology 20 (2014), no. 3, 292-295.

### BibTex

@article {MFAT700,
AUTHOR = {Saeedi, Davod and Nikoufar, Ismail and Saiflu, Husain},
TITLE = {Comment on 'A uniform boundedness theorem for locally convex cones' [W. Roth, Proc. Amer. Math. Soc. 126 (1998), 1973-1982]},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {3},
PAGES = {292-295},
ISSN = {1029-3531},
MRNUMBER = {MR3242710},
ZBLNUMBER = {1324.46017},
URL = {http://mfat.imath.kiev.ua/article/?id=700},
}