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
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References
Kinyanjui JN. Characterization of norm-attainable operators. International Journal of Mathematics Archives. 2018;9(7):124-129.
Lindenstrauss J. On operators which attain their norm. Israel J. Math. 1963;1:139-148.
Okelo NB. Characterization of absolutely norm attaining compact hyponormal operators. Proceedings of
International Mathemacal Sciences. 2020;2.
Okelo NB. Various notions of norm-attainability in normed spaces. Math. FA. 2020;1:1-13.
Okelo NB. Agure JO, Ambogo DO. Norms of elementary operators and characterization of norm - attainable
operators. Int. Journal of Math. Analysis. 2010;24:687-693.
Okelo NB, Aminer JOT. Norm inequalities of norm-attainable operators and their orthogonal extensions.
School of Math. Acturial sci. JOUST Bondo Kenya.
Satish KP, Vern IP. A spectral characterization of AN operators. J. Aust. Math. Soc. 2017;102:369-391.
Shkran S. Norm-attaining operators and Pseudo spectrum. Queens university Belfast, department of pure mathematics. University Road BTT INN BELFAST UK.
Kinyanjui JN, Okelo NB, Ongati O, Musundi SW. Norm estimates for norm-attainable elementary operators. International Journal of Mathematical Analysis. 2018;12:137-144.
Martin M. Norm-attaining compact operators. Department de Analisis Matematico, Universidad de Granada; 2014.
Okelo NB. Norms and norm-attainability of normal operators and their applications. Proceedings of JKUAT Scientific Conference. 2015;83-86.
Okelo NB. The norm-attainability of some elementary operators. Applied Mathematics E-Notes. 2013;13;1- 7.
Ramesh G. Absolutely norm attaining paranormal operators. J. Math. Anal. Applic. 2018;465(1):547-556.