A Characterization of Convex Φ-functions
نویسنده
چکیده
The properties of four elements (LPFE) and (UPFE), introduced by Isac and Persson, have been recently examined in Hilbert spaces, L-spaces and modular spaces. In this paper we prove a new theorem showing that a modular of form ρΦ(f) = R Ω Φ(t, |f(t)|) dμ(t) satisfies both (LPFE) and (UPFE) if and only if Φ is convex with respect to its second variable. A connection of this result with the study of projections and antiprojections onto latticially closed subsets of the modular space L is also discussed.
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