Transitivity of various notions of proximinality in Banach spaces
نویسندگان
چکیده
We derive transitivity of various degrees of proximinality in Banach spaces. When the transitivity does not carry forward to the bigger space we investigate these properties under some additional assumptions of the intermediate space. For instance, we show 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. As a consequence of these properties we derive that in a L1-predual space strongly subdifferentiable points and quasi polyhedral points are same. We also discuss the transitivity of intersection properties of balls in the context of proximinality. Various examples and counter examples are given.
منابع مشابه
Strong proximinality and intersection properties of balls in Banach spaces
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 proxi...
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