Certain Conditions for Norm-Attainability of Elementary Operators and Derivations

Okelo, Bernard; Agure, J. O.; Oleche, Paul Odhiambo

doi:10.26708/ijmsc.2013.1.3.06

Cited by 4 publications

(6 citation statements)

References 3 publications

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“…Additionally, the paper provides insights into the norm of norm-attainable operators, their self-adjointness in Hilbert spaces [9,10], and their prevalence in finite-dimensional spaces. It also uncovers connections between norm-attainable polynomials and extremal points, optimal solutions, and norm-equivalence of operators [11,12 ]. This comprehensive study aims to deepen our understanding of the interplay between functional analysis and optimization, offering a valuable contribution to the field.…”

Section: Introductionmentioning

confidence: 90%

Norm-Attainable Operators and Polynomials: Theory, Characterization, and Applications in Optimization and Functional Analysis

Evans,

Okwany

2023

ARJOM

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This research paper offers a comprehensive investigation into the concept of norm-attainability in Banach and Hilbert spaces. It establishes that norm-attainable operators exist if and only if the target space is a Banach space and that norm-attainable polynomials are inherently linear. In convex optimization scenarios, norm-attainable polynomials lead to unique global optima. The paper explores the norm of norm-attainable operators, revealing its connection to supremum norms. In Hilbert spaces, norm-attainable operators are self-adjoint. Additionally, it shows that in finite-dimensional spaces, all bounded linear operators are norm-attainable. The research also examines extremal polynomials and their relationship with derivative roots, characterizes optimal solutions in norm-attainable operator contexts, and explores equivalence between norm-attainable operators through invertible operators. In inner product spaces, norm-attainable polynomials are identified as constant. Lastly, it highlights the association between norm-attainable operators and convex optimization problems, where solutions lie on the unit ball's boundary. This paper offers a unified perspective with significant implications for functional analysis, operator theory, and optimization in various mathematical and scientific domains.

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Section: Introductionmentioning

confidence: 90%

Norm-Attainable Operators and Polynomials: Theory, Characterization, and Applications in Optimization and Functional Analysis

Evans,

Okwany

2023

ARJOM

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“…The author in [2] further introduced a superclass of the posinormal operators and determined sufficient conditions for this superclass to be posinormal and hyponormal. The idea of norm-attainabilty has also been considered by quite a number of authors, for instance, [4,5] considered conditions for norm-attainability for elementary operators. In this paper, we are interested in characterizing α−supraposinormal operators in dense norm-attainable classes.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, A is norm-attainable if there exists a unit vector x ∈ H such that Ax = A , where . is the usual operator norm [5]. The class of all norm-attainable operators is denoted by NA(H).…”

Section: Introductionmentioning

confidence: 99%

$\alpha$-Supraposinormality of Operators in Dense Norm-Attainable Classes

Okelo

2019

Universal Journal of Mathematics and Applications

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“…Since there is a relationship between the constants A(ξ) and A s ξ of C * -algebras to the ideals and primitive ideals then related results have been given in general Banch settins. Okelo, Agure and Oleche [38] gave results on necessary and sufficient conditions for norm-attainable operators and also studied norm-attainable operators and generalized derivations. Okelo [37] extended the work by presenting new results on conditions that are necessary and sufficient for norm-attainability for operators in Hilbert space, elementary operators and generalized derivations.…”

mentioning

confidence: 99%

“…Okelo [34] characterized norm-attainable classes in terms of orthogonality by giving norm-attainability conditions that were necessary and sufficient for Hilbert space operators first and the orthogonality result on the range and kernel of elementary operators when implemented by norm-attainable operators in norm-attainable classes were also given. Okelo [38] gave conditions for norm-attainability for linear functionals in Banach spaces, non-power operators on H and elementary operators and also gave a new notion of normattainability for power operators then characterized norm-attainable operators in normed spaces.…”

mentioning

confidence: 99%