Norm of Operators on the Generalized Cesàro Matrix Domain

Maryam Sinaei

EN

Norm of Operators on the Generalized Cesàro Matrix Domain

Abstract

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].

Keywords

Hilbert matrix,, Cesàro matrix,, Norm,, Sequence space.

Thanks

Thanks in advanced.

References

[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.
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[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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Maryam Sinaei ^*
Iran

Publication Date

September 29, 2020

Submission Date

August 15, 2020

Acceptance Date

September 22, 2020

Published in Issue

Year 2020 Volume: 3 Number: 3

IZ

https://izlik.org/JA75BP23BX

APA

Sinaei, M. (2020). Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences, 3(3), 155-161. https://izlik.org/JA75BP23BX

AMA

1.Sinaei M. Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences. 2020;3(3):155-161. https://izlik.org/JA75BP23BX

Chicago

Sinaei, Maryam. 2020. “Norm of Operators on the Generalized Cesàro Matrix Domain”. Communications in Advanced Mathematical Sciences 3 (3): 155-61. https://izlik.org/JA75BP23BX.

EndNote

Sinaei M (September 1, 2020) Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences 3 3 155–161.

IEEE

[1]M. Sinaei, “Norm of Operators on the Generalized Cesàro Matrix Domain”, Communications in Advanced Mathematical Sciences, vol. 3, no. 3, pp. 155–161, Sept. 2020, [Online]. Available: https://izlik.org/JA75BP23BX

ISNAD

Sinaei, Maryam. “Norm of Operators on the Generalized Cesàro Matrix Domain”. Communications in Advanced Mathematical Sciences 3/3 (September 1, 2020): 155-161. https://izlik.org/JA75BP23BX.

JAMA

1.Sinaei M. Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences. 2020;3:155–161.

MLA

Sinaei, Maryam. “Norm of Operators on the Generalized Cesàro Matrix Domain”. Communications in Advanced Mathematical Sciences, vol. 3, no. 3, Sept. 2020, pp. 155-61, https://izlik.org/JA75BP23BX.

Vancouver

1.Maryam Sinaei. Norm of Operators on the Generalized Cesàro Matrix Domain. Communications in Advanced Mathematical Sciences [Internet]. 2020 Sep. 1;3(3):155-61. Available from: https://izlik.org/JA75BP23BX

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Abstract

Norm of Operators on the Generalized Cesàro Matrix Domain

Abstract

Keywords

Thanks

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

IZ

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