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

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

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

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


  • 1. A. Maji, P. D. Srivastava, On operator ideals using weightedCesàro sequence space, Journal of the Egyptian Mathematical Society, 22 (2014), 446-452.    
  • 2.A. Grothendieck, Produits Tensoriels Topologiques et Espaces Nucléaires, American Mathematical Soc., 16 (1955).
  • 3.E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen, Mathematische Annalen, 63 (1907), 433-476.    
  • 4.A. Pietsch, Einigie neu Klassen von Kompakten linearenAbbildungen, Revue Roum. Math. Pures et Appl., 8 (1963), 427-447.
  • 5.A. Pietsch, s-Numbers of operators in Banach spaces, StudiaMath., 51 (1974), 201-223.
  • 6.A. Pietsch, Operator Ideals, VEB Deutscher Verlag derWissenschaften, Berlin, 1978.
  • 7.B.Carl, A.Hinrichs, On s-numbers and Weyl inequalities ofoperators in Banach spaces, Bull.Lond. Math. Soc., 41 (2009), 332-340.    
  • 8.A. Pietsch, Eigenvalues and s-numbers, CambridgeUniversity Press, New York, 1986.
  • 9. E. Malkowsky and E. Savaş, Matrix transformations betweensequence spaces of generalized weighted means, Appl. Math. Comput., 147 (2004), 333-345.
  • 10. J. S. Shiue, On the Cesaro sequence spaces, Tamkang J. Math., 1 (1970), 19-25.
  • 11. S. Saejung, Another look at Cesàro sequence spaces, J. Math. Anal. Appl., 366 (2010), 530-537.    
  • 12. G. Constantin, Operators of $ces-p$ type, Rend. Acc. Naz. Lincei., 52 (1972), 875-878.
  • 13. M. Kirişci, The Hahn sequence space defined by the Cesaro mean, Abstr. Appl. Anal., {\bf 2013 (2013), 1-6.
  • 14. N. Tita, On Stolz mappings, Math. Japonica, 26 (1981), 495-496.
  • 15.E. E. Kara, M. İlkhan, On a new class of s-typeoperators, Konuralp Journal of Mathematics, 3 (2015), 1-11.
  • 16.A. Maji, P. D. Srivastava, Some class of operator ideals, Int.J. Pure Appl. Math., 83 (2013), 731-740.
  • 17. S. E. S. Demiriz, The norm of certain matrix operators on the new block sequence space, Conference Proceedings of Science and Technology, 1 (2018), 7-10.
  • 18.A. Maji, P. D. Srivastava, Some results of operator idealson $s-$type $\left \vert A,p\right \vert $ operators, Tamkang J. Math., 45 (2014), 119-136.    
  • 19.N. şimşek,V. Karakaya, H. Polat, Operators idealsof generalized modular spaces of Cesaro type defined by weighted means, J. Comput. Anal. Appl., 19 (2015), 804-811.
  • 20.E. Erdoǧan, V. Karakaya, Operator ideal of s-type operators using weighted mean sequence space, Carpathian J. Math., 33 (2017), 311-318.
  • 21.D. Foroutannia, On the block sequence space $l_p(E)$ andrelated matrix transformations, Turk. J. Math., 39 (2015), 830-841.    
  • 22.H. Roopaei, D. Foroutannia, The norm of certain matrix operatorson new difference sequence spaces, Jordan J. Math. Stat., 8 (2015), 223-237.
  • 23. H. Roopaei, D. Foroutannia, A new sequence space and norm ofcertain matrix operators on this space, Sahand Communications inMathematical Analysis, 3 (2016), 1-12.
  • 24.P. Z. Alp, E. E. Kara, A new class of operator ideals on the block sequence space $l_p(E)$, Adv. Appl. Math. Sci., 18 (2018), 205-217.
  • 25.P. Z. Alp, E. E. Kara, Some equivalent quasinorms on $L_{\phi,E}$, Facta Univ. Ser. Math. Inform., 33 (2018), 739-749.


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