Research Article
BibTex RIS Cite

A New Class of s-type X(u,v;l_p(E)) Operators

Year 2019, , 792 - 800, 01.10.2019
https://doi.org/10.16984/saufenbilder.517762

Abstract

In this
study, we introduce the class of s-type
 X(u,v;l_p(E)) operators, L_(u,v;E).  Also we show that this class is a quasi-Banach operator ideal and we study on
the properties of the classes which are produced via different types of
s-numbers.

References

  • [1] J. Burgoyne, “Denseness of the generalized eigenvectors of a discrete operator in a Banach space,” Journal of Operator Theory,vol.33, pp. 279-297, 1995.
  • [2] B. Carl, A. Hinrichs, “On s-numbers and Weyl inequalities of operators in Banach spaces,” Bulletin of the London Mathematical Society, vol. 41, no. 2, pp. 332-340, 2009.
  • [3] G. Constant "Operators of ces-p-type," Atti Della Academia Nazionale dei Lincei Rendiconti-classe di Scienze Fisiche-Mathematiche & Naturali, vol. 52, no. 6, pp.875-878, 1973.
  • [4] D. Foroutannia, “On the block sequence space lp (E) and related matrix transformations,” Turkish Journal of Mathematics, vol. 39, pp. 830-841, 2015.
  • [5] E. E. Kara, M. İlkhan, “On a new class of s-type operators,” Konuralp Journal of Mathematics, vol. 3, no. 1, pp. 1-11, 2015.
  • [6] A. Maji, P.D. Srivastava, “Some class of operator ideals,” International Journal of Pure and Applied Mathematics, vol. 83, no. 5, pp. 731-740, 2013.
  • [7] A. Maji, P.D. Srivastava, “Some results of operator ideals on s-type |A,p| operators,” Tamkang Journal of Mathematics, vol. 45, no. 2, pp. 119-136, 2014.
  • [8] A. Maji, P.D. Srivastava, “On operator ideals using weighted Cesàro sequence space,” Journal of the Egyptian Mathematical Society, vol. 22, no. 3, pp. 446-452, 2014.
  • [9] A. Pietsch, “Einigie neu Klassen von Kompakten linearen Abbildungen,” Romanian Journal of Pure and Applied Mathematics , vol. 8, pp. 427-447, 1963.
  • [10] A. Pietsch, “Operator Ideals,” VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
  • [11] A. Pietsch, “Eigenvalues and s-numbers,” Cambridge University Press, New York, 1986.
  • [12] A. Pietsch, “s-Numbers of operators in Banach spaces,” Studia Mathematica, vol. 51, no. 3, pp. 201-223,1974.
  • [13] H Roopaei, D Foroutannia, “The norm of certain matrix operators on new difference sequence spaces,” Jordan Journal of Mathematics and Statistics, vol. 8, no. 3, pp. 223 - 237, 2015.
  • [14] H. Roopaei, D Foroutannia, “A new sequence space and norm of certain matrix operators on this space,” Sahand Communications in Mathematical Analysis (SCMA), vol. 3, no. 1, pp. 1-12, 2016.
  • [15] S. Saejung, “Another look at Cesaro sequence spaces,” Journal of Mathematical Analysis and Applications, vol. 366, no. 2, pp. 530–537, 2010.
  • [16] J. S. Shiue, “On the Cesaro sequence spaces,” Tamkang Journal of Mathematics, vol. 1, no. 1, pp. 19–25, 1970.
  • [17] N. Şimşek,V. Karakaya, H. Polat, “Operators ideals of generalized modular spaces of Cesaro type defined by weighted means,” Journal of Computational Analysis and Applications, vol. 19, no. 1, pp. 804-811, 2015.
  • [18] N. Tita, “On Stolz mappings,” Mathematica Japonica, vol. 26, no. 4, pp. 495–496, 1981.
Year 2019, , 792 - 800, 01.10.2019
https://doi.org/10.16984/saufenbilder.517762

Abstract

References

  • [1] J. Burgoyne, “Denseness of the generalized eigenvectors of a discrete operator in a Banach space,” Journal of Operator Theory,vol.33, pp. 279-297, 1995.
  • [2] B. Carl, A. Hinrichs, “On s-numbers and Weyl inequalities of operators in Banach spaces,” Bulletin of the London Mathematical Society, vol. 41, no. 2, pp. 332-340, 2009.
  • [3] G. Constant "Operators of ces-p-type," Atti Della Academia Nazionale dei Lincei Rendiconti-classe di Scienze Fisiche-Mathematiche & Naturali, vol. 52, no. 6, pp.875-878, 1973.
  • [4] D. Foroutannia, “On the block sequence space lp (E) and related matrix transformations,” Turkish Journal of Mathematics, vol. 39, pp. 830-841, 2015.
  • [5] E. E. Kara, M. İlkhan, “On a new class of s-type operators,” Konuralp Journal of Mathematics, vol. 3, no. 1, pp. 1-11, 2015.
  • [6] A. Maji, P.D. Srivastava, “Some class of operator ideals,” International Journal of Pure and Applied Mathematics, vol. 83, no. 5, pp. 731-740, 2013.
  • [7] A. Maji, P.D. Srivastava, “Some results of operator ideals on s-type |A,p| operators,” Tamkang Journal of Mathematics, vol. 45, no. 2, pp. 119-136, 2014.
  • [8] A. Maji, P.D. Srivastava, “On operator ideals using weighted Cesàro sequence space,” Journal of the Egyptian Mathematical Society, vol. 22, no. 3, pp. 446-452, 2014.
  • [9] A. Pietsch, “Einigie neu Klassen von Kompakten linearen Abbildungen,” Romanian Journal of Pure and Applied Mathematics , vol. 8, pp. 427-447, 1963.
  • [10] A. Pietsch, “Operator Ideals,” VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
  • [11] A. Pietsch, “Eigenvalues and s-numbers,” Cambridge University Press, New York, 1986.
  • [12] A. Pietsch, “s-Numbers of operators in Banach spaces,” Studia Mathematica, vol. 51, no. 3, pp. 201-223,1974.
  • [13] H Roopaei, D Foroutannia, “The norm of certain matrix operators on new difference sequence spaces,” Jordan Journal of Mathematics and Statistics, vol. 8, no. 3, pp. 223 - 237, 2015.
  • [14] H. Roopaei, D Foroutannia, “A new sequence space and norm of certain matrix operators on this space,” Sahand Communications in Mathematical Analysis (SCMA), vol. 3, no. 1, pp. 1-12, 2016.
  • [15] S. Saejung, “Another look at Cesaro sequence spaces,” Journal of Mathematical Analysis and Applications, vol. 366, no. 2, pp. 530–537, 2010.
  • [16] J. S. Shiue, “On the Cesaro sequence spaces,” Tamkang Journal of Mathematics, vol. 1, no. 1, pp. 19–25, 1970.
  • [17] N. Şimşek,V. Karakaya, H. Polat, “Operators ideals of generalized modular spaces of Cesaro type defined by weighted means,” Journal of Computational Analysis and Applications, vol. 19, no. 1, pp. 804-811, 2015.
  • [18] N. Tita, “On Stolz mappings,” Mathematica Japonica, vol. 26, no. 4, pp. 495–496, 1981.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Pınar Zengin Alp 0000-0001-9699-7199

Merve İlkhan 0000-0002-0831-1474

Publication Date October 1, 2019
Submission Date January 25, 2019
Acceptance Date March 25, 2019
Published in Issue Year 2019

Cite

APA Zengin Alp, P., & İlkhan, M. (2019). A New Class of s-type X(u,v;l_p(E)) Operators. Sakarya University Journal of Science, 23(5), 792-800. https://doi.org/10.16984/saufenbilder.517762
AMA Zengin Alp P, İlkhan M. A New Class of s-type X(u,v;l_p(E)) Operators. SAUJS. October 2019;23(5):792-800. doi:10.16984/saufenbilder.517762
Chicago Zengin Alp, Pınar, and Merve İlkhan. “A New Class of S-Type X(u,v;L_p(E)) Operators”. Sakarya University Journal of Science 23, no. 5 (October 2019): 792-800. https://doi.org/10.16984/saufenbilder.517762.
EndNote Zengin Alp P, İlkhan M (October 1, 2019) A New Class of s-type X(u,v;l_p(E) Operators. Sakarya University Journal of Science 23 5 792–800.
IEEE P. Zengin Alp and M. İlkhan, “A New Class of s-type X(u,v;l_p(E)) Operators”, SAUJS, vol. 23, no. 5, pp. 792–800, 2019, doi: 10.16984/saufenbilder.517762.
ISNAD Zengin Alp, Pınar - İlkhan, Merve. “A New Class of S-Type X(u,v;L_p(E)) Operators”. Sakarya University Journal of Science 23/5 (October 2019), 792-800. https://doi.org/10.16984/saufenbilder.517762.
JAMA Zengin Alp P, İlkhan M. A New Class of s-type X(u,v;l_p(E)) Operators. SAUJS. 2019;23:792–800.
MLA Zengin Alp, Pınar and Merve İlkhan. “A New Class of S-Type X(u,v;L_p(E)) Operators”. Sakarya University Journal of Science, vol. 23, no. 5, 2019, pp. 792-00, doi:10.16984/saufenbilder.517762.
Vancouver Zengin Alp P, İlkhan M. A New Class of s-type X(u,v;l_p(E)) Operators. SAUJS. 2019;23(5):792-800.

30930 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.