We show that any Banach space X that has a sequence of unit vectors weakly converging to 0 has a closed and bounded convex set that is not remotal. This extends the main result of Sababheh and Khalil, (Numer. Funct. Anal. Optim. 2008; 29:1166-1170)
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets...
AbstractIt is shown that a closed convex bounded subset of a Banach space is weakly compact if and o...
A convex subset B of a real locally convex space X is said to have the separation property if it can...
AbstractWe show that every infinite dimensional Banach space has a closed and bounded convex set tha...
We show that every infinite dimensional Banach space has a closed and bounded convex set that is not...
AbstractWe prove that there exists a weakly closed and bounded subset E of c0 which is not remotal f...
AbstractA self-contained proof is given of the following result.Theorem. Let K be a non-dentable clo...
Let X be an infinite dimensional normed linear space. It is not difficult to see that arbitrarily ne...
AbstractWe consider a definition of a weakly convex set which is a generalization of the notion of a...
It is shown that a closed convex bounded subset of a Banach space is weakly compact if and only if i...
summary:If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences...
We prove that the set of exposed points of a weakly compact and separable convex subset of any Bana...
summary:Every relatively convex-compact convex subset of a locally convex space is contained in a Ba...
AbstractA nonempty closed convex bounded subset C of a Banach space is said to have the weak approxi...
AbstractWe characterize in a reflexive Banach space all the closed convex sets C1 containing no line...
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets...
AbstractIt is shown that a closed convex bounded subset of a Banach space is weakly compact if and o...
A convex subset B of a real locally convex space X is said to have the separation property if it can...
AbstractWe show that every infinite dimensional Banach space has a closed and bounded convex set tha...
We show that every infinite dimensional Banach space has a closed and bounded convex set that is not...
AbstractWe prove that there exists a weakly closed and bounded subset E of c0 which is not remotal f...
AbstractA self-contained proof is given of the following result.Theorem. Let K be a non-dentable clo...
Let X be an infinite dimensional normed linear space. It is not difficult to see that arbitrarily ne...
AbstractWe consider a definition of a weakly convex set which is a generalization of the notion of a...
It is shown that a closed convex bounded subset of a Banach space is weakly compact if and only if i...
summary:If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences...
We prove that the set of exposed points of a weakly compact and separable convex subset of any Bana...
summary:Every relatively convex-compact convex subset of a locally convex space is contained in a Ba...
AbstractA nonempty closed convex bounded subset C of a Banach space is said to have the weak approxi...
AbstractWe characterize in a reflexive Banach space all the closed convex sets C1 containing no line...
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets...
AbstractIt is shown that a closed convex bounded subset of a Banach space is weakly compact if and o...
A convex subset B of a real locally convex space X is said to have the separation property if it can...
DOI
Add to ORKG