Are generalized Lorentz "spaces" really spaces?
We show that the Lorentz space Λ p(ω) need not be a linear set for certain "non-classical" weights ω. We establish necessary and sufficient conditions on p and ω for this situation to occur.
Proceedings of the American Mathematical Society
Ćwikel, M., Kamińska, A., Maligranda, L., & Pick, L. (2004). Are generalized Lorentz "spaces" really spaces?. Proceedings of the American Mathematical Society, 132 (12), 3615-3625. https://doi.org/10.1090/S0002-9939-04-07477-5