Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On Köthe duals of Orlicz-Lorentz spaces (2404.07368v1)

Published 10 Apr 2024 in math.FA

Abstract: In this article, we study a number of properties of the K\"othe duals $\mathcal{M}{\varphi,w}$ of Orlicz-Lorentz spaces. An explicit description of the order-continuous subspace of $\mathcal{M}{\varphi,w}$ is provided. Moreover, the separability of these spaces is characterized by the growth condition $\Delta_2$. Consequently, the K\"othe dual space $\mathcal{M}{\varphi,w}$ has the Radon-Nikod\'ym property if and only if the N-function at infinity $\varphi$ satisfies the appropriate $\Delta_2$-condition. The comparison between $\mathcal{M}{\varphi,w}$ spaces is characterized via standard orders between Orlicz functions. As applications of these results, we provide sufficient conditions for M-embedded order-continuous subspaces of Orlicz-Lorentz spaces equipped with the Luxemburg norm and prove the existence of a unique norm-preserving extension on Orlicz-Lorentz spaces equipped with the Orlicz norm.

Summary

We haven't generated a summary for this paper yet.