Norm-Attainable Operators and Polynomials: Theory, Characterization, and Applications in Optimization and Functional Analysis
Mogoi N. Evans,
Isaac O. Okwany
Abstract:This research paper offers a comprehensive investigation into the concept of norm-attainability in Banach and Hilbert spaces. It establishes that norm-attainable operators exist if and only if the target space is a Banach space and that norm-attainable polynomials are inherently linear. In convex optimization scenarios, norm-attainable polynomials lead to unique global optima. The paper explores the norm of norm-attainable operators, revealing its connection to supremum norms. In Hilbert spaces, norm-attainabl… Show more
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