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Abstract
We prove that every Asplund lush space is generalized-lush using the method of separable
reduction. This gives a partial positive answer to a question by Jan-David Hardtke.
Comments The result concerning separable determination of generalized lushness
is new; however, its application Theorem 1 (Asplund lush space is
generalized-lush) follows from some known results. Namely, using [2, Theorem
2.1 (d) => (c)], every lush Asplund space X satisfies a property from which
one can quite easily deduce that X is generalized lush