Weak coproximinality for banach spaces

Article Type

Research Article

Publication Title

Journal of Nonlinear Functional Analysis


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 Y ⊂ X is a semi-M-ideal in X, then the associated metric projection map is linear and Y is a M-ideal in X. This is also linked to the classical problem of identifying Banach spaces as a quotient space X=Y, where Y has certain non-linear geometric properties in X. 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.

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