Contractive projections on the fixed point set of $L_∞$ contractions

ArticleOriginal scientific text

Title

Authors ¹, ²

Department of Mathematics and Computer Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881, U.S.A.

L_{\infty}

, projection, contraction, binary ball intersection, ergodic, positive operator, fixed point

[AP] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439.
[B] J. B. Baillon, Nonexpansive mappings and hyperconvex spaces, Contemp. Math. 72 (1988), 11-19.
[Br] R. E. Bruck, Jr., A common fixed point theorem for a commuting family of nonexpansive mappings, Pacific J. Math. 53 (1974), 59-71.
[Ka] S. Kakutani, Some characterizations of Euclidean space, Japan. J. Math. 16 (1939), 93-97.
[Kr] U. Krengel, Ergodic Theorems, de Gruyter Stud. Math. 6, Berlin 1985.
[La] H. E. Lacey, The Isometric Theory of Classical Banach Spaces, Springer, Berlin 1974.
[LS] M. Lin and R. Sine, On the fixed point set of nonexpansive order preserving maps, Math. Z. 203 (1990), 227-234.
[LT] J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263-269.
[L1] S. P. Lloyd, An adjoint ergodic theorem, in: Ergodic Theory, F. B. Wright (ed.), Academic Press, 1963, 195-201.
[L2] S. P. Lloyd, Feller boundary induced by a transition operator, Pacific J. Math. 27 (1968), 547-566.
[L3] S. P. Lloyd, Poisson-Martin representation of excessive functions, unpublished manu- script.
[Si] R. C. Sine, On nonlinear contraction semigroups in sup norm spaces, Nonlinear Anal. 3 (1979), 885-890.
[So] P. Soardi, Existence of fixed point of nonexpansive mappings in certain Banach lattices, Proc. Amer. Math. Soc. 73 (1979), 25-29.