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Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$

Year 2019, Volume: 2 Issue: 3, 185 - 188, 30.12.2019

Mehmet Ali Sarıgöl

Abstract

The space $bv$ of bounded variation sequence plays an important role in the summability. More recently this space has been generalized to the space $bv_k^\theta $ and the class $\left( bv_{k}^{\theta },bv\right) $ of infinite matrices has been characterized by Hazar and Sarıgöl [2]. In the present paper, for $1<k<\infty ,$ we give necessary and sufficient conditions for a matrix in the same class to be compact, where $ \theta $ is a sequence of positive numbers.

Keywords

Matrix transformations Sequence spaces $bv_{k}^{\theta }$ spaces

Supporting Institution

the scientific and reseacrh center of Pamukkale University

Project Number

2019KKPP067

References

  • [1] E. Malkowsky, V. Rakocevic, S. Živkovic, Matrix transformations between the sequence space bvk and certain BK spaces, Bull. Cl. Sci. Math. Nat. Sci. Math., 123(27) (2002), 33–46.
  • [2] G. C. Hazar, M. A. Sarıgöl, The space bv k and matrix transformations, 8th International Eurasian Converence on Mathematical Sciences and Applications (IECMSA 2019), 2019 (in press).
  • [3] G. C. Hazar, M. A. Sarıgöl, On absolute Nörlund spaces and matrix operators, Acta Math. Sin. (Engl. Ser.) 34(5) (2018), 812-826.
  • [4] E. Malkowsky, V. Rakocevic, An introduction into the theory of sequence space and measures of noncompactness, Zb. Rad. (Beogr) 9(17) (2000), 143-234.
  • [5] V. Rakocevic, Measures of noncompactness and some applications, Filomat, 12 (1998), 87-120.
  • [6] M. A. Sarıgöl, Extension of Mazhar’s theorem on summability factors, Kuwait Jour. Sci., 42(2) (2015), 28-35.
  • [7] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenraumen Eine Ergebnisüberischt, Math Z., 154 (1977), 1-16.

Year 2019, Volume: 2 Issue: 3, 185 - 188, 30.12.2019

Mehmet Ali Sarıgöl

Abstract

Project Number

2019KKPP067

References

  • [1] E. Malkowsky, V. Rakocevic, S. Živkovic, Matrix transformations between the sequence space bvk and certain BK spaces, Bull. Cl. Sci. Math. Nat. Sci. Math., 123(27) (2002), 33–46.
  • [2] G. C. Hazar, M. A. Sarıgöl, The space bv k and matrix transformations, 8th International Eurasian Converence on Mathematical Sciences and Applications (IECMSA 2019), 2019 (in press).
  • [3] G. C. Hazar, M. A. Sarıgöl, On absolute Nörlund spaces and matrix operators, Acta Math. Sin. (Engl. Ser.) 34(5) (2018), 812-826.
  • [4] E. Malkowsky, V. Rakocevic, An introduction into the theory of sequence space and measures of noncompactness, Zb. Rad. (Beogr) 9(17) (2000), 143-234.
  • [5] V. Rakocevic, Measures of noncompactness and some applications, Filomat, 12 (1998), 87-120.
  • [6] M. A. Sarıgöl, Extension of Mazhar’s theorem on summability factors, Kuwait Jour. Sci., 42(2) (2015), 28-35.
  • [7] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenraumen Eine Ergebnisüberischt, Math Z., 154 (1977), 1-16.
There are 7 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Ali Sarıgöl 0000-0002-9820-1024

Project Number 2019KKPP067
Publication Date December 30, 2019
Acceptance Date December 2, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Sarıgöl, M. A. (2019). Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$. Conference Proceedings of Science and Technology, 2(3), 185-188.
AMA Sarıgöl MA. Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$. Conference Proceedings of Science and Technology. December 2019;2(3):185-188.
Chicago Sarıgöl, Mehmet Ali. “Compact Operators in the Class $\left( {bv_k^\theta ,bv} \right)$”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 185-88.
EndNote Sarıgöl MA (December 1, 2019) Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$. Conference Proceedings of Science and Technology 2 3 185–188.
IEEE M. A. Sarıgöl, “Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 185–188, 2019.
ISNAD Sarıgöl, Mehmet Ali. “Compact Operators in the Class $\left( {bv_k^\theta ,bv} \right)$”. Conference Proceedings of Science and Technology 2/3 (December 2019), 185-188.
JAMA Sarıgöl MA. Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$. Conference Proceedings of Science and Technology. 2019;2:185–188.
MLA Sarıgöl, Mehmet Ali. “Compact Operators in the Class $\left( {bv_k^\theta ,bv} \right)$”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 185-8.
Vancouver Sarıgöl MA. Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$. Conference Proceedings of Science and Technology. 2019;2(3):185-8.
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