On the Pointwise Maximum of Convex Functions
نویسندگان
چکیده
We study the conjugate of the maximum, f ∨ g, of f and g when f and g are proper convex lower semicontinuous functions on a Banach space E. We show that (f ∨g)∗∗ = f∗∗ ∨g∗∗ on the bidual, E∗∗, of E provided that f and g satisfy the Attouch-Brézis constraint qualification, and we also derive formulae for (f ∨ g)∗ and for the “preconjugate” of f∗ ∨ g∗.
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تاریخ انتشار 2000