H. Saiflu
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Comment on 'A uniform boundedness theorem for locally convex cones' [W. Roth, Proc. Amer. Math. Soc. 126 (1998), 1973-1982]
Davod Saeedi, Ismail Nikoufar, Husain Saiflu
Methods Funct. Anal. Topology 20 (2014), no. 3, 292-295
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.
Some results on the uniform boundedness theorem in locally convex cones
Asghar Ranjbari, Husain Saiflu
Methods Funct. Anal. Topology 15 (2009), no. 4, 361-368
Walter Roth studied one form of the uniform boundedness theorem in \cite{Rot98}. We investigate some other versions of the uniform boundedness theorem for barreled and upper-barreled locally convex cones. Finally, we show some applications of this theorem.
A locally convex quotient cone
Asghar Ranjbari, Husain Saiflu
Methods Funct. Anal. Topology 12 (2006), no. 3, 281-285
We define a quotient locally convex cone and verify some topological properties of it. We show that the extra conditions are necessary.
