Coproximinality for Quotient Spaces

  • T.S.S.R.K. Rao

    Indian Statistical Institute, Bangalore, India
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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 ZZ in XX and that of Y/ZY/Z in X/ZX/Z implies the coproximinality of YY in XX, when ZZ is an MM-ideal in XX. For the space C(K)C(K) of continuous functions on a compact extremally disconnected set KK we derive the same conclusion under the assumption that ZZ is an MM-ideal in YY.

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T.S.S.R.K. Rao, Coproximinality for Quotient Spaces. Z. Anal. Anwend. 36 (2017), no. 2, pp. 151–157

DOI 10.4171/ZAA/1583