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

Pınar Zengin Alp; Emrah Evren Kara; Pınar Zengin Alp; Emrah Evren Kara

doi:10.3934/math.2019.3.779

AIMS Mathematics

2019, Volume 4, Issue 3: 779-791. doi: 10.3934/math.2019.3.779

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Research article

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: 09 April 2019 Accepted: 02 June 2019 Published: 05 July 2019
MSC : 47B06, 47B37, 47L20

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.
- 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[J]. AIMS Mathematics, 2019, 4(3): 779-791. doi: 10.3934/math.2019.3.779

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Abstract

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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