# Article

Full entry | PDF   (0.1 MB)
Keywords:
bounded linear maps; extreme points; barrelled spaces
Summary:
In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.
References:
[1] Deville R., Godefroy G., Zizler V.: Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics 64, New York, 1993. MR 1211634 | Zbl 0782.46019
[2] Diestel J.: Sequences and series in Banach spaces. GTM 92, Springer, Berlin, 1984. MR 0737004
[3] Fonf V.P.: Weakly extremal properties of Banach spaces. Math. Notes 45 (1989), 488-494. MR 1019040 | Zbl 0699.46010
[4] Fonf V.P.: On exposed and smooth points of convex bodies in Banach spaces. Bull. London Math. Soc. 28 (1996), 51-58. MR 1356826 | Zbl 0879.46001
[5] Harmand P., Werner D., Werner W.: \$M\$-ideals in Banach spaces and Banach algebras. Springer LNM 1547, Berlin, 1993. MR 1238713 | Zbl 0789.46011
[6] Labuschagne L.E., Mascioni V.: Linear maps between \$C^\ast\$ algebras whose adjoints preserve extreme points of the dual unit ball. Advances in Math. 138 (1998), 15-45. MR 1645056 | Zbl 0944.46054
[7] Rao T.S.S.R.K.: On the extreme point intersection property. ``Function spaces, the second conference'', Ed. K. Jarosz, Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, 1995, pp.339-346. MR 1352241 | Zbl 0868.46011
[8] Wilansky A.: Modern methods in topological vector spaces. McGraw Hill, New York, 1978. MR 0518316 | Zbl 0395.46001

Partner of