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Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$

Year 2022, , 117 - 123, 30.06.2022
https://doi.org/10.47000/tjmcs.1007885

Abstract

In recent paper, the space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ which is the generalization of the absolute Euler Space on the space $l(\mu)$, has been introduced and studied by Gökçe and Sarıgöl [3]. In this study, we give certain characterizations of matrix transformations from the paranormed space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ to one of the classical sequence spaces $c_{0},c,l_{\infty }.$ Also, we show that such matrix operators are bounded linear operators.

References

  • FLett, T.M., On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc., 7 (1957), 113-141.
  • Gökçe, F., Compact and Matrix Operators on the Space $ \left\vert \bar N^{\phi }_p\right\vert _k$, Fundamental Journal of Mathematics and Applications, 4(2)(2021), 124-133.
  • Gökçe, F., Sarıgöl, M.A., On absolute Euler spaces and related matrix operators, Proc. Nat. Acad. Sci. India Sect., A 90(5)(2020), 769-775.
  • Gökçe, F., Sarıgöl, M.A., Generalization of the space l(p) derived by absolute Euler summability and matrix operators, Inequal. Appl., 2018(2018), 133.
  • Gökçe, F., Sarıgöl, M.A., A new series space $ \left\vert \bar N^{\theta }_p\right\vert (\mu)$ and matrix transformations with applications, Kuwait J. Sci., 45(4)(2018), 1-8.
  • Grosse-Erdmann, K.G., Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1993), 223-238.
  • Hazar Güleç, G.C., Compact matrix operators on absolute Cesaro spaces, Numerical Functional Analysis and Optimization, 41(1)(2020), 1-15.
  • Maddox, I. J., Some properties of paranormed sequence spaces, J. London Math. Soc., 2(1969), 316-322.
  • Maddox I. J., Paranormed sequence spaces generated by infinite matrices, Math. Proc. Cambridge Philos. Soc., 64 (1968), 335-340.
  • Maddox I. J., Spaces of strongly summable sequences, Q. J. Math., 18(1947), 345-355.
  • Malkowsky, E., Rakocevic, V., On matrix domains of triangles, Appl.Math. Comp., 189(2)(2007), 1146-1163.
  • Malkowsky, E., Rakocevic, V., An introduction into the theory of sequence space and measures of noncompactness, Zb. Rad.(Beogr), 9(17)(2000), 143-234.
  • Sarıgöl, M.A., Agarwal, R., Banach spaces of absolutely k-summable series, Georgian Mathematical Journal, 2021.
  • Sarıgöl, M.A., Spaces of Series Summable by Absolute Cesaro and Matrix Operators. Comm. Math Appl., 7(1)(2016), 11-22 .
  • Wilansky, A. Summability Through Functional Analysis, Mathematics Studies, 85. North Holland , Amsterdam, 1984.
Year 2022, , 117 - 123, 30.06.2022
https://doi.org/10.47000/tjmcs.1007885

Abstract

References

  • FLett, T.M., On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc., 7 (1957), 113-141.
  • Gökçe, F., Compact and Matrix Operators on the Space $ \left\vert \bar N^{\phi }_p\right\vert _k$, Fundamental Journal of Mathematics and Applications, 4(2)(2021), 124-133.
  • Gökçe, F., Sarıgöl, M.A., On absolute Euler spaces and related matrix operators, Proc. Nat. Acad. Sci. India Sect., A 90(5)(2020), 769-775.
  • Gökçe, F., Sarıgöl, M.A., Generalization of the space l(p) derived by absolute Euler summability and matrix operators, Inequal. Appl., 2018(2018), 133.
  • Gökçe, F., Sarıgöl, M.A., A new series space $ \left\vert \bar N^{\theta }_p\right\vert (\mu)$ and matrix transformations with applications, Kuwait J. Sci., 45(4)(2018), 1-8.
  • Grosse-Erdmann, K.G., Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1993), 223-238.
  • Hazar Güleç, G.C., Compact matrix operators on absolute Cesaro spaces, Numerical Functional Analysis and Optimization, 41(1)(2020), 1-15.
  • Maddox, I. J., Some properties of paranormed sequence spaces, J. London Math. Soc., 2(1969), 316-322.
  • Maddox I. J., Paranormed sequence spaces generated by infinite matrices, Math. Proc. Cambridge Philos. Soc., 64 (1968), 335-340.
  • Maddox I. J., Spaces of strongly summable sequences, Q. J. Math., 18(1947), 345-355.
  • Malkowsky, E., Rakocevic, V., On matrix domains of triangles, Appl.Math. Comp., 189(2)(2007), 1146-1163.
  • Malkowsky, E., Rakocevic, V., An introduction into the theory of sequence space and measures of noncompactness, Zb. Rad.(Beogr), 9(17)(2000), 143-234.
  • Sarıgöl, M.A., Agarwal, R., Banach spaces of absolutely k-summable series, Georgian Mathematical Journal, 2021.
  • Sarıgöl, M.A., Spaces of Series Summable by Absolute Cesaro and Matrix Operators. Comm. Math Appl., 7(1)(2016), 11-22 .
  • Wilansky, A. Summability Through Functional Analysis, Mathematics Studies, 85. North Holland , Amsterdam, 1984.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Fadime Gökçe 0000-0003-1819-3317

Publication Date June 30, 2022
Published in Issue Year 2022

Cite

APA Gökçe, F. (2022). Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$. Turkish Journal of Mathematics and Computer Science, 14(1), 117-123. https://doi.org/10.47000/tjmcs.1007885
AMA Gökçe F. Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$. TJMCS. June 2022;14(1):117-123. doi:10.47000/tjmcs.1007885
Chicago Gökçe, Fadime. “Matrix Operators on the Absolute Euler Space $\left\vert E_{\phi }^{r}\right\vert (\mu)$”. Turkish Journal of Mathematics and Computer Science 14, no. 1 (June 2022): 117-23. https://doi.org/10.47000/tjmcs.1007885.
EndNote Gökçe F (June 1, 2022) Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$. Turkish Journal of Mathematics and Computer Science 14 1 117–123.
IEEE F. Gökçe, “Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$”, TJMCS, vol. 14, no. 1, pp. 117–123, 2022, doi: 10.47000/tjmcs.1007885.
ISNAD Gökçe, Fadime. “Matrix Operators on the Absolute Euler Space $\left\vert E_{\phi }^{r}\right\vert (\mu)$”. Turkish Journal of Mathematics and Computer Science 14/1 (June 2022), 117-123. https://doi.org/10.47000/tjmcs.1007885.
JAMA Gökçe F. Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$. TJMCS. 2022;14:117–123.
MLA Gökçe, Fadime. “Matrix Operators on the Absolute Euler Space $\left\vert E_{\phi }^{r}\right\vert (\mu)$”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 1, 2022, pp. 117-23, doi:10.47000/tjmcs.1007885.
Vancouver Gökçe F. Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$. TJMCS. 2022;14(1):117-23.