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Amemiya norm equals Orlicz norm in general. (English) Zbl 1010.46031

Summary: The authors present a proof that in Orlicz spaces the Amemiya norm and the Orlicz norm coincide for any Orlicz function \(\varphi\). This gives the answer for an open problem. They also give a description of the Amemiya type for the Mazur-Orlicz \(F\)-norm.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A80 Modular spaces
46B42 Banach lattices
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