The new class $L_{z,p,E}$ of $s-$ type operators

Pınar Zengin Alp; Emrah Evren Kara

doi:10.3934/math.2019.3.779

AIMS Mathematics, 2019, 4(3): 779-791. doi: 10.3934/math.2019.3.779. Research article

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The new class $L_{z,p,E}$ of $s-$ type operators

Pınar Zengin Alp, Emrah Evren Kara

Department of Mathematics, Düzce University, Konuralp, Duzce, Turkey

Received: , Accepted: , Published:

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The purpose of this study is to introduce the class of s-type $Z\left(u,v;l_{p}\left( E\right) \right) $ operators, which we denote by $%L_{z,p,E}\left(X,Y\right) $, we prove that this class is an operator ideal and quasi-Banach operator ideal by a quasi-norm defined on this class. Then we define classes using other examples of $ s$-number sequences. We conclude by investigating which of these classes are injective, surjective or symmetric.

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Keywords: block sequence space; operator ideal; s-numbers; quasi-norm

Citation: Pınar Zengin Alp, Emrah Evren Kara. The new class $L_{z,p,E}$ of $s-$ type operators. AIMS Mathematics, 2019, 4(3): 779-791. doi: 10.3934/math.2019.3.779

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