ON THE DUALITY PROBLEM FOR WEAKLY COMPACT, STRICTLY SINGULAR OPERATORS

Abstract

We show that there exists a weakly compact, strictly singular operator T such that the conjugate operator T* is not strictly cosingular. This example gives a negative answer to an old question of Pełczyński.

Mathematics Subject Classification (2000): 47B10.
Quaestiones Mathematicae 28(2005), 37–38.