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

Year 2022, Volume: 12 Issue: 1, 40 - 55, 30.06.2022

Lale Cona

https://doi.org/10.37094/adyujsci.1001762

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.

Keywords

Dual s- numbers, Dual operators, Multiplicative injective and surjective s-numbers, s-numbers, Weyl-Type inequalities

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

Abstract

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.

Keywords

Dual 𝑠-sayıları; Dual operatörler; Çarpımsal injektif ve surjektif 𝑠- sayıları; 𝑠-sayıları; Weyl-Tipi eşitsizlikler.

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