1. CMB 2011 (vol 56 pp. 272)
 Cheng, Lixin; Luo, Zhenghua; Zhou, Yu

On Super Weakly Compact Convex Sets and Representation of the Dual of the Normed Semigroup They Generate
In this note, we first give a characterization of super weakly
compact convex sets of a Banach space $X$:
a closed bounded convex set $K\subset X$ is
super weakly compact if and only if there exists a $w^*$ lower
semicontinuous seminorm $p$ with $p\geq\sigma_K\equiv\sup_{x\in
K}\langle\,\cdot\,,x\rangle$ such that $p^2$ is uniformly FrÃ©chet
differentiable on each bounded set of $X^*$. Then we present a
representation theorem for the dual of the semigroup $\textrm{swcc}(X)$
consisting of all the nonempty super weakly compact convex sets of the
space $X$.
Keywords:super weakly compact set, dual of normed semigroup, uniform FrÃ©chet differentiability, representation Categories:20M30, 46B10, 46B20, 46E15, 46J10, 49J50 

2. CMB 2011 (vol 54 pp. 302)
3. CMB 2009 (vol 52 pp. 28)
4. CMB 2000 (vol 43 pp. 208)
 Matoušková, Eva

Extensions of Continuous and Lipschitz Functions
We show a result slightly more general than the following. Let $K$
be a compact Hausdorff space, $F$ a closed subset of $K$, and $d$ a
lower semicontinuous metric on $K$. Then each continuous function
$f$ on $F$ which is Lipschitz in $d$ admits a continuous extension on
$K$ which is Lipschitz in $d$. The extension has the same supremum
norm and the same Lipschitz constant.
As a corollary we get that a Banach space $X$ is reflexive if and only
if each bounded, weakly continuous and norm Lipschitz function
defined on a weakly closed subset of $X$ admits a weakly continuous,
norm Lipschitz extension defined on the entire space $X$.
Keywords:extension, continous, Lipschitz, Banach space Categories:54C20, 46B10 

5. CMB 1998 (vol 41 pp. 279)
 Acosta, María D.; Galán, Manuel Ruiz

New characterizations of the reflexivity in terms of the set of norm attaining functionals
As a consequence of results due to Bourgain and Stegall, on a
separable Banach space whose unit ball is not dentable, the
set of norm attaining functionals has empty interior (in the
norm topology). First we show that any Banach space can be renormed to
fail this property. Then, our main positive result can be stated as
follows: if a separable Banach space $X$ is very smooth or its bidual
satisfies the $w^{\ast }$Mazur intersection property, then either $X$
is reflexive or the set of norm attaining functionals has empty
interior, hence the same result holds if $X$ has the Mazur
intersection property and so, if the norm of $X$ is Fr\'{e}chet
differentiable. However, we prove that smoothness is not a sufficient
condition for the same conclusion.
Categories:46B04, 46B10, 46B20 
