In this study, we introduce a new double series space $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $ using the four dimensional factorable matrix $ F $ and absolute summability method for $ k\geq 1 $. Also, examining some algebraic and topological properties of $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $, we show that it is norm isomorphic to the well-known double sequence space $ \mathcal{L}_{k} $ for $ 1\leq k < \infty. $ Furthermore, we determine the $ \alpha $-, $ \beta \left(bp\right) $- and $ \gamma $-duals of the spaces $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $ for $ k\geq 1. $ Additionally, we characterize some new four dimensional matrix transformation classes on double series space $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $. Hence, we extend some important results concerned on Riesz and Cesàro matrix methods to double sequences owing to four dimensional factorable matrix.
Citation: Aslıhan ILIKKAN CEYLAN, Canan HAZAR GÜLEÇ. A new double series space derived by factorable matrix and four-dimensional matrix transformations[J]. AIMS Mathematics, 2024, 9(11): 30922-30938. doi: 10.3934/math.20241492
In this study, we introduce a new double series space $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $ using the four dimensional factorable matrix $ F $ and absolute summability method for $ k\geq 1 $. Also, examining some algebraic and topological properties of $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $, we show that it is norm isomorphic to the well-known double sequence space $ \mathcal{L}_{k} $ for $ 1\leq k < \infty. $ Furthermore, we determine the $ \alpha $-, $ \beta \left(bp\right) $- and $ \gamma $-duals of the spaces $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $ for $ k\geq 1. $ Additionally, we characterize some new four dimensional matrix transformation classes on double series space $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $. Hence, we extend some important results concerned on Riesz and Cesàro matrix methods to double sequences owing to four dimensional factorable matrix.
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Aslıhan ILIKKAN CEYLAN, Canan HAZAR GÜLEÇ. A new double series space derived by factorable matrix and four-dimensional matrix transformations[J]. AIMS Mathematics, 2024, 9(11): 30922-30938. doi: 10.3934/math.20241492
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