Are generalized Lorentz “spaces” really spaces? (English) Zbl 1061.46026
Summary: We show that the Lorentz space \(\Lambda^p(w)\) need not be a linear set for certain “non-classical” weights \(w\). We establish necessary and sufficient conditions on \(p\) and \(w\) for this situation to occur.
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 46B42 | Banach lattices |
