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Norm attaining functionals on $C(T)$

Author(s): P. S. Kenderov; W. B. Moors; Scott Sciffer
Journal: Proc. Amer. Math. Soc. 126 (1998), 153-157.
MSC (1991): Primary 46E15
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Abstract: It is shown that for any infinite compact Hausdorff space $T$ , the Bishop-Phelps set in $C(T)^*$ is of the first Baire category when $C(T)$ has the supremum norm.

References:

[1]: J. R. Giles, P. S. Kenderov, W. B. Moors, and Scott Sciffer, Generic differentiability of convex functions on the dual of a Banach space, Pacific J. Math. 172 (1996), 413-431. CMP 96:11
[2]: J. R. Giles and W. B. Moors, Generic continuity of minimal set-valued mappings, preprint.
[3]: I. Namioka, Radon-Nikodým compact space and fragmentability, Mathematika 34 (1987), 258-281. MR 89i:46021
[4]: Z. Semadeni, Banach spaces of continuous functions, Vol. 1, PWN, Warszawa, 1971. MR 45:5730
[5]: John L. Kelley, General Topology, D. Van Nostrand, 1955. MR 16:1136c
[6]: W. B. Moors, The relationship between Goldstine's theorem and the convex point of continuity property, J. Math. Anal. and Appl. 188 (1994), 819-832. MR 95k:46024


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