Coproximinality for quotient spaces

Article Type

Research Article

Publication Title

Zeitschrift für Analysis und ihre Anwendungen

Abstract

In this paper we study the classical notion of coproximinality, for quotient spaces of Banach spaces. We provide a partial solution to the three space problem, analogous to a classical result of Cheney and Wulbert, by showing that for Z-Y X; coproximinality of Z in X and that of Y=Z in X=Z implies the coproximinality of Y in X, when Z is an M-ideal in X. For the space C(K) of continuous functions on a compact extremally disconnected set K we derive the same conclusion under the assumption that Z is an M-ideal in Y .

First Page

151

Last Page

157

DOI

10.4171/ZAA/1583

Publication Date

1-1-2017

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