In this paper, two main results concerning uniformly continuous retractions are proved. First, an $\alpha$-H\"older retraction from any separable Banach space onto a compact convex subset whose closed linear span is the whole space is constructed for every positive $\alpha<1$. This constitutes a positive solution to a H\"older version of a question raised by Godefroy and Ozawa. In fact, compact convex sets are found to be absolute $\alpha$-H\"older retracts under certain assumption of flatness. Second, we provide an example of a strictly convex Banach space $X$ arbitrarily close to $\ell_2$ (for the Banach Mazur distance) and a finite dimensional compact convex subset of $X$ for which the nearest point map is not uniformly continuous even w...
If C is a convex subset of a Banach space E, a projection is a retraction r of C onto a subset F whi...
summary:Every relatively convex-compact convex subset of a locally convex space is contained in a Ba...
We show that any Banach space X that has a sequence of unit vectors weakly converging to 0 has a clo...
Abstract. We characterize metric spaces X whose hyperspaces 2X or Bd(X) of non-empty closed (bounded...
AbstractFor a Banach space B and for a class A of its bounded closed retracts, endowed with the Haus...
Let X be an infinite-dimensional uniformly convex Banach space and let BX and SX be its closed unit ...
Abstract. The dual space X ∗ of a Banach space X is said to admit a uniformly simul-taneously contin...
In our note we show the very close connection between the existence of a Finite Dimensional Decompo...
We show that every infinite dimensional Banach space has a closed and bounded convex set that is not...
AbstractWe show that every infinite dimensional Banach space has a closed and bounded convex set tha...
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continu...
AbstractWe prove a new inequality valid in any two-dimensional normed space. As an application, it i...
AbstractWe characterize complete metric absolute (neighborhood) retracts in terms of existence of ce...
A convex subset B of a real locally convex space X is said to have the separation property if it can...
It is shown that a closed convex bounded subset of a Banach space is weakly compact if and only if i...
If C is a convex subset of a Banach space E, a projection is a retraction r of C onto a subset F whi...
summary:Every relatively convex-compact convex subset of a locally convex space is contained in a Ba...
We show that any Banach space X that has a sequence of unit vectors weakly converging to 0 has a clo...
Abstract. We characterize metric spaces X whose hyperspaces 2X or Bd(X) of non-empty closed (bounded...
AbstractFor a Banach space B and for a class A of its bounded closed retracts, endowed with the Haus...
Let X be an infinite-dimensional uniformly convex Banach space and let BX and SX be its closed unit ...
Abstract. The dual space X ∗ of a Banach space X is said to admit a uniformly simul-taneously contin...
In our note we show the very close connection between the existence of a Finite Dimensional Decompo...
We show that every infinite dimensional Banach space has a closed and bounded convex set that is not...
AbstractWe show that every infinite dimensional Banach space has a closed and bounded convex set tha...
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continu...
AbstractWe prove a new inequality valid in any two-dimensional normed space. As an application, it i...
AbstractWe characterize complete metric absolute (neighborhood) retracts in terms of existence of ce...
A convex subset B of a real locally convex space X is said to have the separation property if it can...
It is shown that a closed convex bounded subset of a Banach space is weakly compact if and only if i...
If C is a convex subset of a Banach space E, a projection is a retraction r of C onto a subset F whi...
summary:Every relatively convex-compact convex subset of a locally convex space is contained in a Ba...
We show that any Banach space X that has a sequence of unit vectors weakly converging to 0 has a clo...
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