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The New Class $L_{p,\Phi}$ of $s$-Type Operators

Year 2023, Volume: 6 Issue: 4, 162 - 169, 18.12.2023
https://doi.org/10.32323/ujma.1378917

Abstract

In this study, the class of $s$-type $\ell_{p}( \Phi )$ operators is introduced and it is shown that $L_{p,\Phi}$ is a quasi-Banach operator ideal. Also, some other classes are defined by using approximation, Gelfand, Kolmogorov, Weyl, Chang, and Hilbert number sequences. Then, some properties are examined.

References

  • [1] A. Maji, P. D. Srivastava, On operator ideals using weighted Cesaro sequence space, Egyptian Math. Soc., 22(3) (2014), 446-452.
  • [2] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, Amer. Math. Soc., 16 (1955).
  • [3] E. E. Kara, M. ˙Ilkhan, On a new class of s-type operators, Konuralp J. Math., 3(1) (2015), 1-11.
  • [4] A. Maji, P. D. Srivastava, Some class of operator ideals, Int. J. Pure Appl. Math., 83(5) (2013), 731-740.
  • [5] A. Maji, P. D. Srivastava, Some results of operator ideals on s􀀀type jA; pj operators, Tamkang J. Math., 45(2) (2014), 119-136.
  • [6] N. Şimşek, V. Karakaya, H. Polat, Operators ideals of generalized modular spaces of Cesaro type defined by weighted means, J. Comput. Anal. Appl., 19(1) (2015), 804-811.
  • [7] E. Erdoğan, V. Karakaya, Operator ideal of s-type operators using weighted mean sequence space, Carpathian J. Math., 33(3) (2017), 311-318.
  • [8] P. Zengin Alp, E. E. Kara, A new class of operator ideals on the block sequence space lp(E), Adv. Appl. Math. Sci. 18(2) (2018), 205-217.
  • [9] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen, Math. Ann., 63(4) (1907), 433–476.
  • [10] A. Pietsch, Einigie neu klassen von kompakten linearen abbildungen, Revue Roum. Math. Pures et Appl., 8 (1963), 427-447.
  • [11] A. Pietsch, s􀀀Numbers of operators in Banach spaces, Studia Math., 51(3) (1974), 201-223.
  • [12] A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
  • [13] B. Carl, A. Hinrichs, On s-numbers and Weyl inequalities of operators in Banach spaces, Bull. Lond. Math. Soc., 41(2) (2009), 332-340.
  • [14] A. Pietsch, Eigenvalues and s􀀀numbers, Cambridge University Press, New York, 1986.
  • [15] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford, 18(2) (1967), 345-355.
  • [16] G. Constantin, Operators of ces-p type, Rend. Acc. Naz. Lincei., 52(8) (1972), 875-878.
  • [17] N. Tita, On Stolz mappings, Math. Japonica, 26(4) (1981), 495–496.
  • [18] E. Kovac, On f convergence and f density, Mathematica Slovaca, 55 (2005), 329-351.
  • [19] M. ˙Ilkhan, A new Banach space defined by Euler totient matrix operator, Oper. Matrices, 13(2) (2019), 527-544.
Year 2023, Volume: 6 Issue: 4, 162 - 169, 18.12.2023
https://doi.org/10.32323/ujma.1378917

Abstract

References

  • [1] A. Maji, P. D. Srivastava, On operator ideals using weighted Cesaro sequence space, Egyptian Math. Soc., 22(3) (2014), 446-452.
  • [2] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, Amer. Math. Soc., 16 (1955).
  • [3] E. E. Kara, M. ˙Ilkhan, On a new class of s-type operators, Konuralp J. Math., 3(1) (2015), 1-11.
  • [4] A. Maji, P. D. Srivastava, Some class of operator ideals, Int. J. Pure Appl. Math., 83(5) (2013), 731-740.
  • [5] A. Maji, P. D. Srivastava, Some results of operator ideals on s􀀀type jA; pj operators, Tamkang J. Math., 45(2) (2014), 119-136.
  • [6] N. Şimşek, V. Karakaya, H. Polat, Operators ideals of generalized modular spaces of Cesaro type defined by weighted means, J. Comput. Anal. Appl., 19(1) (2015), 804-811.
  • [7] E. Erdoğan, V. Karakaya, Operator ideal of s-type operators using weighted mean sequence space, Carpathian J. Math., 33(3) (2017), 311-318.
  • [8] P. Zengin Alp, E. E. Kara, A new class of operator ideals on the block sequence space lp(E), Adv. Appl. Math. Sci. 18(2) (2018), 205-217.
  • [9] E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen, Math. Ann., 63(4) (1907), 433–476.
  • [10] A. Pietsch, Einigie neu klassen von kompakten linearen abbildungen, Revue Roum. Math. Pures et Appl., 8 (1963), 427-447.
  • [11] A. Pietsch, s􀀀Numbers of operators in Banach spaces, Studia Math., 51(3) (1974), 201-223.
  • [12] A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
  • [13] B. Carl, A. Hinrichs, On s-numbers and Weyl inequalities of operators in Banach spaces, Bull. Lond. Math. Soc., 41(2) (2009), 332-340.
  • [14] A. Pietsch, Eigenvalues and s􀀀numbers, Cambridge University Press, New York, 1986.
  • [15] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford, 18(2) (1967), 345-355.
  • [16] G. Constantin, Operators of ces-p type, Rend. Acc. Naz. Lincei., 52(8) (1972), 875-878.
  • [17] N. Tita, On Stolz mappings, Math. Japonica, 26(4) (1981), 495–496.
  • [18] E. Kovac, On f convergence and f density, Mathematica Slovaca, 55 (2005), 329-351.
  • [19] M. ˙Ilkhan, A new Banach space defined by Euler totient matrix operator, Oper. Matrices, 13(2) (2019), 527-544.
There are 19 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Pınar Zengin Alp 0000-0001-9699-7199

Early Pub Date December 11, 2023
Publication Date December 18, 2023
Submission Date October 20, 2023
Acceptance Date December 10, 2023
Published in Issue Year 2023 Volume: 6 Issue: 4

Cite

APA Zengin Alp, P. (2023). The New Class $L_{p,\Phi}$ of $s$-Type Operators. Universal Journal of Mathematics and Applications, 6(4), 162-169. https://doi.org/10.32323/ujma.1378917
AMA Zengin Alp P. The New Class $L_{p,\Phi}$ of $s$-Type Operators. Univ. J. Math. Appl. December 2023;6(4):162-169. doi:10.32323/ujma.1378917
Chicago Zengin Alp, Pınar. “The New Class $L_{p,\Phi}$ of $s$-Type Operators”. Universal Journal of Mathematics and Applications 6, no. 4 (December 2023): 162-69. https://doi.org/10.32323/ujma.1378917.
EndNote Zengin Alp P (December 1, 2023) The New Class $L_{p,\Phi}$ of $s$-Type Operators. Universal Journal of Mathematics and Applications 6 4 162–169.
IEEE P. Zengin Alp, “The New Class $L_{p,\Phi}$ of $s$-Type Operators”, Univ. J. Math. Appl., vol. 6, no. 4, pp. 162–169, 2023, doi: 10.32323/ujma.1378917.
ISNAD Zengin Alp, Pınar. “The New Class $L_{p,\Phi}$ of $s$-Type Operators”. Universal Journal of Mathematics and Applications 6/4 (December 2023), 162-169. https://doi.org/10.32323/ujma.1378917.
JAMA Zengin Alp P. The New Class $L_{p,\Phi}$ of $s$-Type Operators. Univ. J. Math. Appl. 2023;6:162–169.
MLA Zengin Alp, Pınar. “The New Class $L_{p,\Phi}$ of $s$-Type Operators”. Universal Journal of Mathematics and Applications, vol. 6, no. 4, 2023, pp. 162-9, doi:10.32323/ujma.1378917.
Vancouver Zengin Alp P. The New Class $L_{p,\Phi}$ of $s$-Type Operators. Univ. J. Math. Appl. 2023;6(4):162-9.

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