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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2022 / Cilt: 12 - Sayı: 1

New Weyl-Type Inequalities by Multiplicative Injective and Surjective s-Numbers of Operators in Reflexive Banach Spaces

Yansımalı Banach Uzaylarda Operatörlerin Çarpımsal İnjektiv ve Surjektiv s-Sayıları ile Yeni Weyl-Tipi Eşitsizlikleri

Lale CONA
Pages
40–55
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

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

So, new Weyl-type inequalities are investigated for both dual 𝑠-number sequences and dual operators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, two problems are investigated.
📊
Key Findings & Data:In general, Weyl-type inequalities of operators in complex reflexive Banach spaces are discussed.
💡
Conclusion & Impact:So, new Weyl-type inequalities are investigated for both dual 𝑠-number sequences and dual operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work, two problems are investigated. In general, Weyl-type inequalities of operators in complex reflexive Banach spaces are discussed. First, we obtained the Weyl-type inequalities using arbitrary multiplicative surjective and injective 𝑠-numbers that are dual of each other. Second, we introduced the Weyl-type inequalities by multiplicative injective and surjective 𝑠- numbers under certain conditions for 𝑆 and 𝑆^' operators in complex reflexive Banach space. So, new Weyl-type inequalities are investigated for both dual 𝑠-number sequences and dual operators.

Özet

Bu çalışmada iki problem incelenmiştir. Genel olarak, kompleks yansımalı Banach uzaylarında operatörlerin Weyl-tipi eşitsizlikleri üzerinde durulmuştur. İlk olarak, birbirinin duali olan keyfi çarpımsal surjektif ve injektif 𝑠-sayılarını kullanarak Weyl-tipi eşitsizlikler elde edilmiştir. İkinci olarak, kompleks yansımalı Banach uzayındaki 𝑆 ve 𝑆$ operatörleri için belirli koşullar altında çarpımsal injektif ve surjektif 𝑠-sayıları ile Weyl-tipi eşitsizlikler ifade edilmiştir. Böylece hem dual 𝑠-sayı dizileri hem de dual operatörler için yeni Weyl-tipi eşitsizlikleri araştırılmıştır.

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Cite This Article

CONA, L. (2022). New Weyl-Type Inequalities by Multiplicative Injective and Surjective s-Numbers of Operators in Reflexive Banach Spaces. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 12 - Sayı: 1, 40–55. https://ajindex.com/articles/428394

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