Long-standing open problems of Banach space theory: My personal top ten

Abstract

Every serious scientist wants to discover fundamental results. However, due to outer circumstances expressed by the slogan ‘publish or perish,’ the reality looks quite different: too many mathematicians are led to deal only with problems that promise a quick and successful solution. This attitude is a decisive reason why every mature mathematical theory includes a comprehensive list of challenging problems that are open for a long time, say 25 years. It is the goal of this paper to provide such a list for the theory of Banach spaces. The enumeration of the problems does not indicate any ranking.

*This is an elaborated version of two lectures delivered at the University of Pretoria in April 2008.