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Journals / Turkish Journal of Mathematics / 2009 / Cilt: 33 - Sayı: 2

Perturbation of Closed Range Operators

Ghadir SADEGHİ
Sal Mohammad MOSLEHİAN
Pages
143–149
Publication Date
2022-11-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X.
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Key Findings & Data:The operator A is called T-bounded if |Ax|\leq a|x|+b|Tx| for some a, b\geq 0 and all x \in D(T).
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Conclusion & Impact:Thus we establish a link between T-bounded operators and Hyers--Ulam stability.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hilbert space · perturbation · Hyers--Ulam stability

Abstract

Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X. The operator A is called T-bounded if |Ax|\leq a|x|+b|Tx| for some a, b\geq 0 and all x \in D(T). If A has the Hyers--Ulam stability then under some suitable assumptions we show that both T and S: = A+T have the Hyers--Ulam stability. We also discuss the best constant of Hyers--Ulam stability for the operator S. Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

Özet

Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X. The operator A is called T-bounded if |Ax|\leq a|x|+b|Tx| for some a, b\geq 0 and all x \in D(T). If A has the Hyers--Ulam stability then under some suitable assumptions we show that both T and S: = A+T have the Hyers--Ulam stability. We also discuss the best constant of Hyers--Ulam stability for the operator S. Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

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Cite This Article

SADEGHİ, G., MOSLEHİAN, S. M. (2022). Perturbation of Closed Range Operators. Turkish Journal of Mathematics, Cilt: 33 - Sayı: 2, 143–149. https://ajindex.com/articles/608576

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References (10)

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  10. Dordrecht, Boston and London, 2003. Mohammad Sal MOSLEHIAN1,2, Ghadir SADEGHI1,2 Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box, Mashhad 91775, IRAN e-mail: [email protected] and [email protected] Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad-IRAN e-mail: [email protected]