Abstract
We present two families of L-matrices and investigate their properties using intricate factorization techniques. These factorization schemes involve well-known matrices such as the classical Cesàro, Gamma, Hausdorff, and Hilbert matrices, which are utilized to assess the norm of L-matrices. Additionally, these factorizations give rise to novel and intriguing inequalities in sequence spaces.
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References
Bennett, G.: Factorizing the classical inequalities. Mem. Am. Math. Soc. 576 (1996)
Bennett, G.: Lower bounds for matrices II. Canad. J. Math. 44, 54–74 (1992)
Bouthat, L., Mashreghi, J.: The critical point and the \(p\)-norm of the Hilbert \(L\)-matrix. Linear Algebra Appl. 634, 1–14 (2022)
Chen, C.P., Luor, D.C., Ou, Z.Y.: Extensions of Hardy inequality. J. Math. Anal. Appl. 273, 160–171 (2002)
Foroutannia, D., Roopaei, H.: The norms of certain matrix operators from \(\ell _p\) spaces into \(\ell _p(\Delta ^n)\) spaces. Linear Multilinear Algebra 67(4), 767–776 (2019)
Gao, P.: A note on \(\ell ^p\) norms of weighted mean matrices. J. Inequal. Appl. 2012(110), 1–7 (2012)
Hardy, G.H.: Divergent Series. Oxford University Press, Oxford (1973)
Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, 2nd edn. Cambridge University Press, Cambridge (2001)
Kara, M.I., Roopaei, H.: A weighted mean Hausdorff type operator and its summability matrix domain. J. Inequal. Appl. Article number 27 (2022)
Roopaei, H.: Factorization of Cesàro operator and related inequalities. J. Inequal. Appl. Article number 177 (2021)
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Mashreghi, J., Roopaei, H. Factorization of Infinite L-matrices. Results Math 78, 207 (2023). https://doi.org/10.1007/s00025-023-01996-2
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DOI: https://doi.org/10.1007/s00025-023-01996-2