Coproximinality for quotient spaces

Rao, T. S. S. R. K. (2017) Coproximinality for quotient spaces Zeitschrift fur Analysis und ihre Anwendungen, 36 . pp. 151-157. ISSN 0232-2064

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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⊂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.

Item Type:Article
Source:Copyright of this article belongs to European Mathematical Society.
Keywords:Best Coapproximation; Hilbert Spaces; Quotient Spaces
ID Code:112411
Deposited On:10 Jan 2018 04:26
Last Modified:10 Jan 2018 10:40

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