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In this paper, we investigate some properties of the domains (Formula presented.) and (Formula presented.) of the Gamma matrix of order n in the classical spaces (Formula presented.) c 0, c and (Formula presented.) of absolutely p-summable, null, convergent and bounded sequences, respectively, and compute the α-, β- and γ-duals of these spaces. We characterize the classes of infinite matrices from the space (Formula presented.) to the spaces (Formula presented.) and f, and from a normed sequence space to the gamma sequence spaces (Formula presented.) and (Formula presented.) Moreover, we introduce the necessary and sufficient conditions for factorizing an operator based on the weighted mean matrices and derive the factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Finally, we emphasize on the lower bound of operators from (Formula presented.) into (Formula presented.) from (Formula presented.) into (Formula presented.) from (Formula presented.) into itself and from (Formula presented.) into itself. © 2022 Taylor & Francis Group, LLC. |
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