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

Yıl 2023, , 162 - 169, 18.12.2023
https://doi.org/10.32323/ujma.1378917

Öz

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.

Kaynakça

  • [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.
Yıl 2023, , 162 - 169, 18.12.2023
https://doi.org/10.32323/ujma.1378917

Öz

Kaynakça

  • [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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Pınar Zengin Alp 0000-0001-9699-7199

Erken Görünüm Tarihi 11 Aralık 2023
Yayımlanma Tarihi 18 Aralık 2023
Gönderilme Tarihi 20 Ekim 2023
Kabul Tarihi 10 Aralık 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

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. Aralık 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, sy. 4 (Aralık 2023): 162-69. https://doi.org/10.32323/ujma.1378917.
EndNote Zengin Alp P (01 Aralık 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., c. 6, sy. 4, ss. 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 (Aralık 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, c. 6, sy. 4, 2023, ss. 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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