In this paper the author uses the game characterization of fragmentability and sigmafragmentability developed by P. S. Kenderov and W. B. Moors [J. London Math. Soc. (2) 60 (1999), no. 1, 203–223; MR1721825 (2001f:46025)] to show that if a compact space X with the tree-completeness property contains a disjoint sequence of non-empty clopen sets, then (C(X), weak) is not sigma-fragmented by the norm. In particular, this means that C(X) does not admit any equivalent Kadets renorming [see J. E. Jayne, I. Namioka and C. A. Rogers, Mathematika 39 (1992), no. 1, 161–188; MR1176478 (93i:46027)]. This paper is interesting and well written.

Keywords