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On the lower semi-continuity of the set valued metric projection. (English) Zbl 0759.41019

The author first discusses some results on the finite order intersection properties of cells and makes use of the results to study the lower semi- continuity of best approximations operators from Banach lattices on to closed ideals. He further investigates the existence of best approximation to sub-function modulus of functions modules.

MSC:

41A30 Approximation by other special function classes
41A28 Simultaneous approximation
41A50 Best approximation, Chebyshev systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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