Normability of Lorentz spaces—an alternative approach
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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 Λ. Furthermore, we also use this method in the weak case and characterize normability of Λ v ∞ . Finally, we characterize the linearity of the space Λ v ∞ by a simple condition on the weight v.
Keywordsweighted Lorentz space weighted inequality non-increasing rearrangement Banach function space associate space
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