"Exotic" constructions in Banach spaces - Kazimierz Goebel (University of Lublin)

Abstract:

It is obvious and well known fact that the geometry and topology of finite dimensional Banach spaces changes substantially when we pass to the case of infinite dimension. This is caused mainly by the fact that bounded and closed subsets of infinite dimensional space are, not necessarily compact. Especially all balls are not compact. In consequence of that, many classical theorems valid in finite dimensional spaces fail in this more general setting. Within the category of infinite dimensional Banach spaces, there are also differences caused by the regularity of geometries induced by the selection of the norm. In the talk we present a number examples related to fixed point theory and illustrating such situations.