Strong proximinality and intersection properties of balls in Banach spaces
نویسندگان
چکیده
We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z ⊆ Y ⊆ X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M -ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proximinal subspace Y of X is strongly proximinal in X if and only if Y ⊥⊥ is strongly proximinal in X. We also prove that in an abstract L1-space, the notions of strongly subdifferentiable points and quasipolyhedral points coincide. We also give an example to show that M -ideals need not be ball proximinal. Moreover, we prove that in an L1-predual space, M -ideals are ball proximinal.
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Transitivity of various notions of proximinality in Banach spaces
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