1. Normability of Lorentz spaces—an alternative approach
- Creator:
- Gogatishvili, Amiran and Soudský, Filip
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- weighted Lorentz space, weighted inequality, non-increasing rearrangement, Banach function space, and associate space
- Language:
- English
- Description:
- 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 $v$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public