GENERALIZED α-KÖTHE TOEPLITZ DUALS OF CERTAIN DIFFERENCE SEQUENCE SPACES
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초록
In this paper, we compute the generalized $\alpha$-K\"{o}the Toeplitz duals of the $X$-valued (Banach space) difference sequence spaces $E(X,\Delta)$, $E(X,\Delta_v)$ and obtain a generalization of the existing results for $\alpha$-duals of the classical difference sequence spaces $E(\Delta)$ and $E(\Delta_v)$ of scalars, $E \in \{ \ell_\infty,c,c_0 \}$. Apart from this, we compute the generalized $\alpha$-Köthe Toeplitz duals for $E(X,\Delta^r)\; r\geq0$ integer and observe that the results agree with corresponding results for scalar cases.
Abstract
In this paper, we compute the generalized $\alpha$-K\"{o}the Toeplitz duals of the $X$-valued (Banach space) difference sequence spaces $E(X,\Delta)$, $E(X,\Delta_v)$ and obtain a generalization of the existing results for $\alpha$-duals of the classical difference sequence spaces $E(\Delta)$ and $E(\Delta_v)$ of scalars, $E \in \{ \ell_\infty,c,c_0 \}$. Apart from this, we compute the generalized $\alpha$-Köthe Toeplitz duals for $E(X,\Delta^r)\; r\geq0$ integer and observe that the results agree with corresponding results for scalar cases.
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