Norm attaining operators and renormings of Banach spaces (Q795277)

A Banach space X has property A (resp. property B) if for every Banach space Y the norm attaining operators from X to Y are dense in L(X,Y) (resp. the norm attaining operators from Y to X are dense in L(Y,X)). It was shown by J. Partington that - surprisingly! - every Banach space may be equivalently renormed to have property B. In the present paper it is shown by an argument ''predual'' to that of Partington, that many Banach spaces (e.g. all separable ones) may be renormed to have property A. This shows in particular that property A is not equivalent to the Radon- Nikodym-property. Finally an example of a Banach space, due to S. Shelah, is given which may not be renormed to have property A.