Quantitative Analysis and Algebra of Norm-Attainability in Operators in Approximation Theory
Mogoi N. Evans *
Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Kenya.
Samuel B. Apima
Department of Mathematics and Statistics, Kaimosi Friends University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
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 operators, convexity of the distance function, and convergence rates for sequences of approximations. We also establish optimality conditions and error bounds for norm approximations, providing new insights into their geometric and analytical behavior. Applications in approximation theory, including spectral and compact operator approximations, are explored, emphasizing practical relevance and computational efficiency.
Keywords: Norm-attainable operators, operator norm topology, distance minimization, convergence analysis, approximation theory, quantitative operator analysis