Partial Mielnik Spaces and Characterization of Uniformly Convex Spaces
Copyright policy )Partial Mielnik Spaces and Characterization of Uniformly Convex Spaces
We characterize uniform convexity of normed linear spaces in terms of a functional inequality generalizing Clarkson’s inequality for L p {L_p} spaces. This inequality can be interpreted as saying that the unit sphere of the space carries a structure slightly weaker than a probability space in the sense of Mielnik. From this point of view, our result is analogous to an earlier characterization of inner product spaces. We also investigate briefly the abstract concept of partial probability space suggested by the main result.
Isomorphic theory (including renorming) of Banach spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Isomorphic theory (including renorming) of Banach spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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