Research article

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

  • 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.

    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

    Related Papers:

  • 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.


    加载中


    [1] A. Maji, P. D. Srivastava, On operator ideals using weightedCesàro sequence space, Journal of the Egyptian Mathematical Society, 22 (2014), 446-452. doi: 10.1016/j.joems.2013.10.005
    [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. doi: 10.1007/BF01449770
    [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. doi: 10.1112/blms/bdp007
    [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. doi: 10.1016/j.jmaa.2010.01.029
    [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. doi: 10.5556/j.tkjm.45.2014.1297
    [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. doi: 10.3906/mat-1501-16
    [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.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4059) PDF downloads(853) Cited by(3)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog