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arXiv · 2510.24290

Maximal non-compactness of embeddings between sequence spaces

Anna Kneselová
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Abstract

We will focus on studying the ball measure of non-compactness $\alpha(T)$ for various particular instances of embedding operators in sequence spaces. Our first main goal is to find necessary and sufficient conditions for an identity operator to be maximally non-compact. Next, we will focus on studying Lorentz sequence spaces $\ell^{p,q}$ and their basic properties. We will characterize the inclusions between Lorentz sequence spaces depending on the values of $p$ and $q$. Then we will try to determine exact values of the norms of the identity operators between these embedded spaces. Lastly, we will determine whether these identity operators are maximally non-compact by using our general theorems.

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Anna Kneselová. 2025-10-28. Maximal non-compactness of embeddings between sequence spaces. https://arxiv.org/abs/2510.24290

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