Let $T: S_X \rightarrow S_Y$ be an onto isometry between the unit spheres of two (real) Banach spaces, and $C \subseteq S_X$ a maximal convex subset of $S_X$. Is it true that $T(C)$ is also a convex set of $S_Y$?
2026-04-01 16:20:16.1775060416
invariance of convex sets
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