Weak∗ closures and derived sets in dual Banach spaces

نویسندگان

  • Mikhail I. Ostrovskii
  • Vincenzo Bruno Moscatelli
چکیده

The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subset A ⊂ X∗ such that A 6= A ∗ (the latter denotes the weak∗ closure of A). (3) Let X be a quasi-reflexive Banach space and A ⊂ X∗ be an absolutely convex subset. Then A = A ∗ .

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تاریخ انتشار 2010