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

Yıl 2019, Cilt: 23 Sayı: 5, 792 - 800, 01.10.2019

Pınar Zengin Alp Merve İlkhan

https://doi.org/10.16984/saufenbilder.517762

Öz

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.

Anahtar Kelimeler

operator ideals, s-numbers, block sequence spaces

Kaynakça

• [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.