Directional uniform rotundity in spaces of essentially bounded functions.
Smith's counterexample about uniform rotundity in every direction.
It is an open question when the direct sum of normed spaces inherits uniform rotundity in every direction from the factor spaces. M. Smith [4] showed that, in general, the answer is negative. The purpose of this paper is to carry out a complete study of Smith's counterexample.
Relative rotundity in Lp(X).
Continuity of the uniform rotundity modulus relative to linear subspaces
We prove the continuity of the rotundity modulus relative to linear subspaces of normed spaces. As a consequence we reduce the study of uniform rotundity relative to linear subspaces to the study of the same property relative to closed linear subspaces of Banach spaces.
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