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


How to Cite

Evans, Mogoi N., and Samuel B. Apima. 2023. “Properties and Characterizations of Norm-Attainable Operators in Compact and Self-Adjoint Settings”. Asian Research Journal of Mathematics 19 (10):96-102. https://doi.org/10.9734/arjom/2023/v19i10731.