A relationship between the 112-ball property and the strong 112-ball property

Abstract

AbstractThe 112-ball property and the strong 112-ball property in a Banach space were studied by D. Yost [Bull. Austral. Math. Soc. 20 (1979), 285–300; Math. Scand. 50 (1982), 100–110]. G. Godini [“Banach Space Theory and Its Applications” (A. Pietsch, N. Popa and I. Singer, Eds.), Vol. 991, Springer-Verlag, New York/Berlin, 1983], gave geometrical characterizations of the subspaces with property (∗), as well as with the 112-ball property. D. Yost [Math. Scand. 50 (1982), 100–110] gave an example that has the 112-ball property but not the strong 112-ball property. In the present paper, property (S) is introduced and characterizations of the strong 112-ball property are given. The subspaces of C(T) which have the 112-ball property are characterized, where T is compact and connected