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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.03211 |
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Table of Contents:
- In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is strictly and uniformly convex. We also prove that when $ 1\le q_-,p_-,q_+,p_+<\infty, $ the convergence in norm implies the convergence in measure, and under some conditions on exponents, the approximation identity holds in the space $ \ell^1(L^{\frac{p(\cdot)}{q(\cdot)}}) $.