Properties and Characterizations of Norm-Attainable Operators in Compact and Self-Adjoint Settings
Mogoi N. Evans *
Department of Mathematics and Statistics, Kaimosi Friends University, Kenya.
Samuel B. Apima
Department of Mathematics and Statistics, Kaimosi Friends University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this research paper, we investigate the properties and characterizations of norm-attainable operators in the context of compactness and self-adjointness. We present a series of propositions, a lemma, a theorem, and a corollary that shed light on the nature of these operators and provide insights into their behavior in various settings. Our results contribute to the understanding of norm-attainable operators and their implications in functional analysis.
Keywords: Compact operators, numerical range, function spaces, normal operators, self-adjoint operators, functional calculus, reflexive spaces, finite-dimensional spaces