Compactness of Matrix Operators on the Banach Space $\ell_p(T)$

Merve İlkhan [1] , Emrah Evren Kara [2]

28 121

In this study, by using the Hausdorff measure of non-compactness, we obtain the necessary and sufficient conditions for certain matrix operators on the spaces $\ell_p(T)$ and $\ell_\infty(T)$ to be compact, where $1\leq p<\infty$.
Compact operators, Hausdorff measure of non-compactness, Sequence spaces
  • [1] E. Malkowsky, V. Rakocevic, An introduction into the theory of sequence spaces and measure of noncompactness, Zbornik radova, Matematicki Inst. SANU, Belgrade, 9(17) (2000), 143–234.
  • [2] V. Rakocevic, Measures of noncompactness and some applications, Filomat, 12(2) (1998), 87–120.
  • [3] M. Başarır, E. E. Kara, On compact operators on the Riesz B(m)-difference sequence spaces, Iran. J. Sci. Technol., 35(A4) (2011), 279–285.
  • [4] M. Başarır, E. E. Kara, On some difference sequence spaces of weighted means and compact operators, Ann. Funct. Anal., 2 (2011), 114–129.
  • [5] M. Başarır, E. E. Kara, On the B-difference sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., 391 (2012), 67–81.
  • [6] M. Mursaleen, V. Karakaya, H. Polat, N. Şimşek, Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means, Comput. Math. Appl., 62 (2011), 814–820.
  • [7] M. Mursaleen, S. A. Mohiuddine, Applications of measures of noncompactness to the infinite system of differential equations in $\ell_p$ spaces, Nonlinear Anal., 75 (2012), 2111–2115.
  • [8] M. Mursaleen, A. K. Noman, Applications of Hausdorff measure of noncompactness in the spaces of generalized means, Math. Inequal. Appl., 16(1) (2013), 207–220.
  • [9] M. Mursaleen, A. K. Noman, The Hausdorff measure of noncompactness of matrix operators on some BK spaces, Oper. Matrices, 5(3) (2011), 473–486.
  • [10] E. E. Kara, M. İlkhan, On some Banach sequence spaces derived by a new band matrix, Br. J. Math. Comput. Sci. 9(2) (2015), 141–159.
  • [11] M. Mursaleen, A. K. Noman, Compactness by the Hausdorff measure of noncompactness, Nonlinear Anal., 73(8) (2010), 2541–2557.
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-0831-1474
Author: Merve İlkhan (Primary Author)
Country: Turkey


Orcid: 0000-0002-6398-4065
Author: Emrah Evren Kara

Dates

Publication Date: December 14, 2018

Bibtex @conference paper { cpost482378, journal = {Conference Proceedings of Science and Technology}, issn = {2651-544X}, address = {Murat TOSUN}, year = {2018}, volume = {1 (2018)}, pages = {11 - 15}, doi = {}, title = {Compactness of Matrix Operators on the Banach Space \$\\ell\_p(T)\$}, key = {cite}, author = {İlkhan, Merve and Kara, Emrah Evren} }
APA İlkhan, M , Kara, E . (2018). Compactness of Matrix Operators on the Banach Space $\ell_p(T)$. Conference Proceedings of Science and Technology, 1 (2018) (1), 11-15. Retrieved from http://dergipark.org.tr/cpost/issue/41126/482378
MLA İlkhan, M , Kara, E . "Compactness of Matrix Operators on the Banach Space $\ell_p(T)$". Conference Proceedings of Science and Technology 1 (2018) (2018): 11-15 <http://dergipark.org.tr/cpost/issue/41126/482378>
Chicago İlkhan, M , Kara, E . "Compactness of Matrix Operators on the Banach Space $\ell_p(T)$". Conference Proceedings of Science and Technology 1 (2018) (2018): 11-15
RIS TY - JOUR T1 - Compactness of Matrix Operators on the Banach Space $\ell_p(T)$ AU - Merve İlkhan , Emrah Evren Kara Y1 - 2018 PY - 2018 N1 - DO - T2 - Conference Proceedings of Science and Technology JF - Journal JO - JOR SP - 11 EP - 15 VL - 1 (2018) IS - 1 SN - 2651-544X- M3 - UR - Y2 - 2018 ER -
EndNote %0 Conference Proceedings of Science and Technology Compactness of Matrix Operators on the Banach Space $\ell_p(T)$ %A Merve İlkhan , Emrah Evren Kara %T Compactness of Matrix Operators on the Banach Space $\ell_p(T)$ %D 2018 %J Conference Proceedings of Science and Technology %P 2651-544X- %V 1 (2018) %N 1 %R %U
ISNAD İlkhan, Merve , Kara, Emrah Evren . "Compactness of Matrix Operators on the Banach Space $\ell_p(T)$". Conference Proceedings of Science and Technology 1 (2018) / 1 (December 2018): 11-15.
AMA İlkhan M , Kara E . Compactness of Matrix Operators on the Banach Space $\ell_p(T)$. Conference Proceedings of Science and Technology. 2018; 1 (2018)(1): 11-15.
Vancouver İlkhan M , Kara E . Compactness of Matrix Operators on the Banach Space $\ell_p(T)$. Conference Proceedings of Science and Technology. 2018; 1 (2018)(1): 15-11.