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- W3005534612 abstract "We make some remarks on the global shape of continuous convex functions defined on a Banach space Z. For instance we show that if Z is separable then for every continuous convex function f:Z→R there exists a unique closed linear subspace Yf of Z such that, for the quotient space Xf:=Z/Yf and the natural projection π:Z→Xf, the function f can be written in the formf(z)=φ(π(z))+ℓ(z)for allz∈Z, where ℓ∈X⁎ and φ:Xf→R is a convex function such that limt→∞φ(x+tv)=∞ for every x,v∈Xf with v≠0. This kind of result is generally false if Z is nonseparable (even in the Hilbertian case Z=ℓ2(Γ) with Γ an uncountable set)." @default.
- W3005534612 created "2020-02-24" @default.
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- W3005534612 date "2020-06-01" @default.
- W3005534612 modified "2023-10-01" @default.
- W3005534612 title "On the global shape of continuous convex functions on Banach spaces" @default.
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- W3005534612 doi "https://doi.org/10.1016/j.jmaa.2020.123944" @default.
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