Summary
Let X be a rotund, reflexive Banach space, M⊆X a closed subspace and PM: X→M the best approximation operator on M. This paper deals with some aspects of the general question of how PM may be constructed out of simpler operators. A class of operators called B-operators, which generalize best approximation operators, is defined and conditions are given under which PM is the limit of sequences of B-operators. Several examples and applications are also included.
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Entrata in Redazione il 20 novembre 1974.
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Sullivan, F. A generalization of best approximation operators. Annali di Matematica 107, 245–261 (1975). https://doi.org/10.1007/BF02416475
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DOI: https://doi.org/10.1007/BF02416475