Maximal non-compactness of embeddings between sequence spaces

2025/10/28 by Kneselová, Anna
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.24290

Abstract

We will focus on studying the ball measure of non-compactness α(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 ℓ^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.

Related

• Compactness in Lorentz sequence spaces
• Compactness of Embeddings
• Measures of Noncompactness in N(p,q) Summable Sequence Spaces
• Maximal noncompactness of embeddings into Marcinkiewicz spaces
• Entropy numbers of finite-dimensional Lorentz space embeddings