Coproximinality for quotient spaces
Zeitschrift für Analysis und ihre Anwendungen
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 .
Rao, T. S.S.R.K., "Coproximinality for quotient spaces" (2017). Journal Articles. 2782.