On this note, we investigate the quantitative aspects of norm-attainability in operators, focusing on distances to the set of norm-attainable operators, rates of convergence, and approximation properties. Key results include the structural characterization of norm-attainable oper...
Open access
Research Article10.9734/air/2025/v26i31345
This research paper delves into Sobolev spaces and function spaces on smooth manifolds, revealing fundamental theorems such as existence, embeddings, and compactness properties. Noteworthy results include the Poincare inequality elucidating function behavior on compact manifolds...
Open access
Research Article10.9734/air/2024/v25i31060
This research paper explores various properties and implications of norm-attainable operators on Hilbert spaces. We establish lemmas, propositions, and theorems that shed light on the characteristics of these operators and their relationship with the geometry and structure of the...
Open access
Research Article10.9734/air/2024/v25i11019
This research paper explores various properties of Sobolev spaces on compact manifolds, focusing on embedding theorems, compactness, and inequalities. We establish the compact embedding of Sobolev spaces into continuous and Lebesgue spaces, as well as the continuity and compactne...
Open access
Research Article10.9734/air/2024/v25i11014