Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2017-03-29
Coproximinality for Quotient SpacesT.S.S.R.K. Rao (1) Indian Statistical Institute, Bangalore, India
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 $Z \subset Y \subset X$, 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 $Y$.
Keywords: Best coapproximation, Hilbert spaces, quotient spaces
Rao T.S.S.R.K.: Coproximinality for Quotient Spaces. Z. Anal. Anwend. 36 (2017), 151-157. doi: 10.4171/ZAA/1583