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Received June 19, 2016; Accepted December 28, 2016; Published January 5, 2017
Abstract. In this paper, we introduce a weaker form of the classical notion of coproximinality for Banach spaces. This is intended as a new tool to make the metric projection map linear. We show that if a weakly coproximinal subspace is a semi--ideal in , then the associated metric projection map is linear and is a -ideal in . This is also linked to the classical problem of identifying Banach spaces as a quotient space , where has certain non-linear geometric properties in . We give a counterexample to the 3-space problem for weak coproximinality. We also study its stability properties for spaces of vector-valued continuous functions.
How to Cite this Article:
T. S. S. R. K. Rao, Weak coproximinality for Banach spaces, Journal of Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 13, pp. 1-10.