This paper presents a nonlinear spectral framework for analyzing monotone and nonexpansive operators in Banach and Hilbert spaces. We construct a nonlinear spectral resolution for maximal monotone operators using Yosida approximations and Fitzpatrick functions, leading to a famil...
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Research Article10.9734/acri/2025/v25i61272
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...
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Research Article10.9734/air/2025/v26i31345
This paper presents a comprehensive investigation into the norm attainability of compact operators on infinitedimensional Hilbert spaces, offering novel spectral and geometric insights. We establish necessary and sufficient conditions for norm attainment in terms of the spectral...
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Research Article10.9734/acri/2025/v25i41158
This paper examines the relationship between frame operators, dual frames, and norm attainability in Hilbert spaces. Frames are basis-like systems that span a vector space while allowing linear dependency, enabling the achievement of desirable properties not available with orthon...
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Research Article10.9734/ajarr/2025/v19i3946
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...
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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...
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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...
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Research Article10.9734/air/2024/v25i11014