| Abstrakt: |
Abstract: We study normability properties of classical Lorentz spaces. Given a certain general lattice-like structure, we first prove a general sufficient condition for its associate space to be a Banach function space. We use this result to develop an alternative approach to Sawyer's characterization of normability of a classical Lorentz space of type $\Lambda$. Furthermore, we also use this method in the weak case and characterize normability of $\Lambda_v^{\infty}$. Finally, we characterize the linearity of the space $\Lambda_v^{\infty}$ by a simple condition on the weight $v$. |
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