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Combination of linear and multiplicative structures gives an algebra. What if instead of a linear structure one has a convex one? Is there a term for this?

A natural example is provided, for instance, by the space of all probability measures on a group (with the multiplicative operation provided by convolution).

R W
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  • "Convex algebra" sounds good to me, although it might provoke confusion with the term "locally convex algebra," which I believe means a topological algebra which is locally convex as a topological vector space. Another natural class of examples are the unit balls of Banach algebras. – Qiaochu Yuan Nov 12 '14 at 08:27
  • I also thought about "convex algebra", but couldn't find a single use. – R W Nov 12 '14 at 11:46

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