room: A1-33, godz. 10:30–12:00

Anibala Molto (University of Valencia, Spain)
C(K) spaces with good renorming properties

Summary. We will consider, for some compacta \(K\), the behaviour of \(C(K)\), the Banach space of its continuous functions on \(K\), with respect to the existence of an equivalent locally uniformly rotund (LUR) or a Kadets norm. It is well known any LUR norm is a Kadets one and, in turn, if a Banach space \(X\) has a Kadets norm then \(X\) has a countable cover by sets of small local \(\|\cdot\|\)-diameter (SLD). Some classes of compacta \(K\) for which \(C(K)\) has some of those properties will be presented, studying the topological properties of \(K\) that allow to deduce some of those good renormings on \(C(K)\).

Tea and coffee at 10:00.