Research Article

- [1] F. Başar, Domain of the composition of some triangles in the space of p-summable sequences, AIP Conference Proceedings, 1611 (2014), 348–356.
- [2] F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monograph, Istanbul–2012.
- [3] B. Altay, F. Başar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336(1) (2007), 632–645.
- [4] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc., 576(1996).
- [5] G. Bennett, Lower bounds for matrices, Linear Algebra Appl., 82(1986), 81-98.
- [6] C. P. Chen, D. C. Luor, and Z. y. Ou, Extensions of Hardy inequality, J. Math. Anal. Appl. 273 (2002), 160–171.
- [7] G. H. Hardy, Divergent Series, Oxford University press, 1973.
- [8] G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, 2nd edition, Cambridge University press, Cambridge, 2001.
- [9] M. İlkhan, Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space, Math. Methods Appl. Sci., 42(16) (2019), 5143-5153.
- [10] P. N. Ng, P. Y. Lee, Cesaro sequence spaces of non-absolute type, Comment. Math. Prace Mat. 20(2) (1978), 429-433.
- [11] H. Roopaei and D. Foroutannia, The norm of matrix operators on Ces`aro weighted sequence space, Linear Multilinear Algebra, 67 (1) (2019), 175-185.
- [12] H. Roopaei and D. Foroutannia, The norms of certain matrix operators from `p spaces into p(Dn) spaces, Linear Multilinear Algebra, 67 (4) (2019), 767-776.
- [13] H. Roopaei, Factorization of Cesaro and Hilbert matrices based on generalized Cesaro matrix, Linear Multilinear Algebra, 68 (1) (2020), 193-204.
- [14] H. Roopaei, Factorization of the Hilbert matrix based on Ces`aro and Gamma matrices, Results Math, 75(1) (2020), 3, published online.
- [15] H. Roopaei, Norms of summability and Hausdorff mean matrices on difference sequence spaces, Math. Inequal. Appl., 22 (3) (2019), 983-987.
- [16] H. Roopaei, D. Foroutannia, M. İlkhan, E. E. Kara, Cesaro Spaces and Norm of Operators on These Matrix Domains, Mediterr. J. Math., 17 (2020), 121.
- [17] H. Roopaei, Norm of Hilbert operator on sequence spaces, J. Inequal. Appl. 2020 (2020), 117.
- [18] H. Roopaei, A study on Copson operator and its associated sequence spaces, J. Inequal. Appl. 2020:120, (2020).
- [19] H. Roopaei, Bounds of operators on the Hilbert sequence space, Concr. Oper. (7) (2020), 155–165.
- [20] M. Şengönül, F. Başar, Cesaro sequence spaces of non-absolute type which include the spaces c0 and c, Soochow J. Math., 31(1) (2005), 107-119.

Roopaei in [13] has introduced some factorization for the infinite Hilbert matrix and

the Cesàro matrix of order n based on the generalized Cesàro matrix. In this research,

we investigate the norm of these two operators on the generalized Cesàro matrix domain.

Moreover we introduce some factorizations for the Hilbert matrix. Hence the present study

is a complement of Roopaei’s research. There are several new Banach spaces who have

introduced and studied by using matrix domains of special lower triangular matrices. For more

references we encourage the readers to some papers [1, 3, 17, 18] and textbook [2].

the Cesàro matrix of order n based on the generalized Cesàro matrix. In this research,

we investigate the norm of these two operators on the generalized Cesàro matrix domain.

Moreover we introduce some factorizations for the Hilbert matrix. Hence the present study

is a complement of Roopaei’s research. There are several new Banach spaces who have

introduced and studied by using matrix domains of special lower triangular matrices. For more

references we encourage the readers to some papers [1, 3, 17, 18] and textbook [2].

Thanks in advanced.

- [1] F. Başar, Domain of the composition of some triangles in the space of p-summable sequences, AIP Conference Proceedings, 1611 (2014), 348–356.
- [2] F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monograph, Istanbul–2012.
- [3] B. Altay, F. Başar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336(1) (2007), 632–645.
- [4] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc., 576(1996).
- [5] G. Bennett, Lower bounds for matrices, Linear Algebra Appl., 82(1986), 81-98.
- [6] C. P. Chen, D. C. Luor, and Z. y. Ou, Extensions of Hardy inequality, J. Math. Anal. Appl. 273 (2002), 160–171.
- [7] G. H. Hardy, Divergent Series, Oxford University press, 1973.
- [8] G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, 2nd edition, Cambridge University press, Cambridge, 2001.
- [9] M. İlkhan, Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space, Math. Methods Appl. Sci., 42(16) (2019), 5143-5153.
- [10] P. N. Ng, P. Y. Lee, Cesaro sequence spaces of non-absolute type, Comment. Math. Prace Mat. 20(2) (1978), 429-433.
- [11] H. Roopaei and D. Foroutannia, The norm of matrix operators on Ces`aro weighted sequence space, Linear Multilinear Algebra, 67 (1) (2019), 175-185.
- [12] H. Roopaei and D. Foroutannia, The norms of certain matrix operators from `p spaces into p(Dn) spaces, Linear Multilinear Algebra, 67 (4) (2019), 767-776.
- [13] H. Roopaei, Factorization of Cesaro and Hilbert matrices based on generalized Cesaro matrix, Linear Multilinear Algebra, 68 (1) (2020), 193-204.
- [14] H. Roopaei, Factorization of the Hilbert matrix based on Ces`aro and Gamma matrices, Results Math, 75(1) (2020), 3, published online.
- [15] H. Roopaei, Norms of summability and Hausdorff mean matrices on difference sequence spaces, Math. Inequal. Appl., 22 (3) (2019), 983-987.
- [16] H. Roopaei, D. Foroutannia, M. İlkhan, E. E. Kara, Cesaro Spaces and Norm of Operators on These Matrix Domains, Mediterr. J. Math., 17 (2020), 121.
- [17] H. Roopaei, Norm of Hilbert operator on sequence spaces, J. Inequal. Appl. 2020 (2020), 117.
- [18] H. Roopaei, A study on Copson operator and its associated sequence spaces, J. Inequal. Appl. 2020:120, (2020).
- [19] H. Roopaei, Bounds of operators on the Hilbert sequence space, Concr. Oper. (7) (2020), 155–165.
- [20] M. Şengönül, F. Başar, Cesaro sequence spaces of non-absolute type which include the spaces c0 and c, Soochow J. Math., 31(1) (2005), 107-119.

Primary Language | English |
---|---|

Subjects | Mathematical Sciences |

Journal Section | Articles |

Authors | |

Publication Date | September 29, 2020 |

Submission Date | August 15, 2020 |

Acceptance Date | September 22, 2020 |

Published in Issue | Year 2020 Volume: 3 Issue: 3 |

Bibtex | @research article { cams780899, journal = {Communications in Advanced Mathematical Sciences}, issn = {2651-4001}, address = {}, publisher = {Emrah Evren KARA}, year = {2020}, volume = {3}, number = {3}, pages = {155 - 161}, title = {Norm of Operators on the Generalized Cesàro Matrix Domain}, key = {cite}, author = {Sinaei, Maryam} } |

APA | Sinaei, M. (2020). Norm of Operators on the Generalized Cesàro Matrix Domain . Communications in Advanced Mathematical Sciences , 3 (3) , 155-161 . Retrieved from https://dergipark.org.tr/en/pub/cams/issue/56960/780899 |

MLA | Sinaei, M. "Norm of Operators on the Generalized Cesàro Matrix Domain" . Communications in Advanced Mathematical Sciences 3 (2020 ): 155-161 <https://dergipark.org.tr/en/pub/cams/issue/56960/780899> |

Chicago | Sinaei, M. "Norm of Operators on the Generalized Cesàro Matrix Domain". Communications in Advanced Mathematical Sciences 3 (2020 ): 155-161 |

RIS | TY - JOUR T1 - Norm of Operators on the Generalized Cesàro Matrix Domain AU - MaryamSinaei Y1 - 2020 PY - 2020 N1 - DO - T2 - Communications in Advanced Mathematical Sciences JF - Journal JO - JOR SP - 155 EP - 161 VL - 3 IS - 3 SN - 2651-4001- M3 - UR - Y2 - 2020 ER - |

EndNote | %0 Communications in Advanced Mathematical Sciences Norm of Operators on the Generalized Cesàro Matrix Domain %A Maryam Sinaei %T Norm of Operators on the Generalized Cesàro Matrix Domain %D 2020 %J Communications in Advanced Mathematical Sciences %P 2651-4001- %V 3 %N 3 %R %U |

ISNAD | Sinaei, Maryam . "Norm of Operators on the Generalized Cesàro Matrix Domain". Communications in Advanced Mathematical Sciences 3 / 3 (September 2020): 155-161 . |

AMA | Sinaei M. Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences. 2020; 3(3): 155-161. |

Vancouver | Sinaei M. Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences. 2020; 3(3): 155-161. |

IEEE |
M. Sinaei
,
"Norm of Operators on the Generalized Cesàro Matrix Domain",
Communications in Advanced Mathematical Sciences,
vol. 3,
no. 3,
pp.
155-161, Sep. 2020 |

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