Roopaei, H.Ilkhan, M.2021-12-012021-12-0120212299-3282https://doi.org/10.1515/conop-2020-0112https://hdl.handle.net/20.500.12684/10619In 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.en10.1515/conop-2020-0112info:eu-repo/semantics/closedAccessCesaro matrixHilbert matrixGamma matrixNormSequence spaceArticle8124392-s2.0-85102267077WOS:000640603000001Q3N/A