CONVERGENCES FOR SEQUENCES OF SETS AND LINEAR MAPPINGS

[摘要] Let E, F be normed vector spaces and let A, A, be continuous linear operators from E into F. Consider X, X(n) [Y, Y-n] arbitrary nonempty closed subsets of E [F]. We study the problem: if X = lim X(n) [Y = lim Y-n] in the sense of Kuratowski (or Mosco, or Attouch-Wets), do we have A(X) = lim A(X,) [A(-1)(Y) = lim A(n)(-1)(Y-n)] in the same sense ? In solving this problem we improve recent results obtained by I. Schochetman and R. Smith and published in this journal, and extend some results of G. Beer established for the case F = R. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01