Best approximation in L(X, Y)

Let X, Y be Banach spaces and G a closed subspace of Y. Let L(X, Y) be the space of bounded linear operators from X into Y. In this paper we investigate when L(X, G) is proximal in L(X, Y). Further, we discuss the related problem of proximinality of L∞(T, G) in L∞(T, Y). We improve results obtained...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 1988-11, Vol.104 (3), p.527-531
Main Authors: Deeb, W., Khalil, R.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
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Summary:Let X, Y be Banach spaces and G a closed subspace of Y. Let L(X, Y) be the space of bounded linear operators from X into Y. In this paper we investigate when L(X, G) is proximal in L(X, Y). Further, we discuss the related problem of proximinality of L∞(T, G) in L∞(T, Y). We improve results obtained by Light and Cheney in this direction.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100065713