Norm-Attainable Operators in Hilbert Spaces: Properties and Applications
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
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 underlying Hilbert space. These results have applications in functional analysis, linear algebra, and operator theory.
Keywords: Functional analysis, operator theory, Hilbert spaces, norm-attainable operators, range of an operator, Kernel of an operator, compact operators, unitary operators, closed operators, Banach-Alaoglu theorem