There are no denting points

in the unit ball of

Author:
T. S. S. R. K. Rao

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2969-2973

MSC (1991):
Primary 46B20, 46E40

DOI:
https://doi.org/10.1090/S0002-9939-99-04941-2

Published electronically:
April 28, 1999

MathSciNet review:
1610781

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For an infinite compact set and for any Banach space we show that the unit ball of the space of -valued functions that are continuous when is equipped with the weak topology, has no denting points.

**[De]**J.A. De Reyna, J. Diestel, V. Lomonosov and L.R. Piazza, Some observations about the space of weakly continuous functions from a compact space into a Banach space, Questiones Mathematicae 15 (1992), 415-425. MR**94b:46055****[DU]**J. Diestel and J.J. Uhl, Vector measures, Math. Surveys, No. 15, Providence, Rhode Island, 1977. MR**56:12216****[D]**J. Diestel, Sequences and Series in Banach spaces, GTM, No. 92, Springer, Berlin, 1984. MR**85i:46020****[DS]**N. Dunford and J.T. Schwartz, Linear operators, Part I: General Theory, Interscience publishers, New York, 1958. MR**90g:47001a**(Reprint)**[E]**G. Emmanuele, Remarks on weak compactness of operators defined on certain injective tensor products, Proc. Amer. Math. Soc., 116 (1992), 473-476. MR**92m:46109****[G]**R. Gr[??]a\'{s}lewicz, Extreme operator valued continuous maps, Arkiv for Matematik 29 (1991), 73-81. MR**92h:46049****[H]**R.B. Holmes, Geometric functional analysis and its applications, GTM, No. 24, Springer, Berlin, 1975. MR**53:14085****[LLT]**Bor-Luh Lin, Pei-Kee Lin and S.L. Troyanski, Characterizations of denting points, Proc. Amer. Math. Soc. 102 (1988), 526-528. MR**89e:46016****[L]**H.E. Lacey, The isometric theory of classical Banach spaces, Springer, Berlin, 1974. MR**58:12308****[R1]**T.S.S.R.K. Rao, A note on extreme points of , J. Ramanujan Math. Soc. 9 (1994), 215-219. MR**95j:46039****[R2]**T.S.S.R.K. Rao, On a theorem of Dunford, Pettis and Phillips, Real Analysis Exchange 20 (1994/5), 741-743. MR**96d:46057****[S]**M. Sharir, Characterization and properties of extreme operators into , Israel J. Math. 12 (1972) 174-183. MR**47:5574**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
46B20,
46E40

Retrieve articles in all journals with MSC (1991): 46B20, 46E40

Additional Information

**T. S. S. R. K. Rao**

Affiliation:
Indian Statistical Institute, R.V. College Post, Bangalore 560 059, India

Email:
tss@isibang.ac.in

DOI:
https://doi.org/10.1090/S0002-9939-99-04941-2

Keywords:
Denting point,
vector valued continuous functions

Published electronically:
April 28, 1999

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1999
American Mathematical Society