The Banach-Saks properties in Orlicz-Lorentz spaces. (English) Zbl 1468.46040
Summary: The Banach-Saks index of an Orlicz-Lorentz space \(\Lambda_{\varphi, w}(I)\) for both function and sequence case, is computed with respect to its Matuszewska-Orlicz indices of \(\varphi\). It is also shown that an Orlicz-Lorentz function space has weak Banach-Saks (resp., Banach-Saks) property if and only if it is separable (resp., reflexive).
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
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