On a Sufficient Condition for Proximity
نویسنده
چکیده
A closed subspace M in a Banach space X is called t/-proximinal if it satisfies: (1 + p)S n (S + M) ç S + e(pXS n M), for some positive valued function t(p), p > 0, and e(p) -» 0 as p -> 0, where 5 is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are (/-proximinal, for example, the subspaces with the 2-ball property (semi M-ideals) and certain subspaces of compact operators in the spaces of bounded linear operators.
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