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Cesaro Spaces and Norm of Operators on These Matrix Domains
(Springer Basel Ag, 2020) Roopaei, H.; Foroutannia, D.; Ilkhan, M.; Kara, E. E.
In this paper, we investigate some properties of the domain of the Cesaro matrix of ordernand compute Kothe dual of this space. Moreover, we compute the norm of well-known operators such as Hilbert, Hausdorff, backward difference and weighted mean operators on this new sequence space.
Fractional Cesaro Matrix and its Associated Sequence Space
(De Gruyter Poland Sp Z O O, 2021) Roopaei, H.; Ilkhan, M.
In this research, we introduce a new fractional Cesaro matrix and investigate the topological properties of the sequence space associated with this matrix. We also introduce a fractional Gamma matrix as well and obtain some factorizations for the Hilbert operator based on Cesaro and Gamma matrices. The results of these factorizations are two new inequalities one of which is a generalized version of the well-known Hilbert's inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.