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Matrix domain of the triangle in $l_p$, $1\leq p\leq \infty
Last modified: 2014-02-19
Abstract
The sequence spaces $C_0(\Delta_u^\lambda)$ and
$C(\Delta_u^\lambda)$ have been recently introduced and studied. In
present paper, following the similar approach, we define a new
sequence spaces $l_p(\Delta_u^\lambda)$, $1\leq p \leq \infty$ and
by applying the general methods as in [E.Malkowsky, V. Rakocevi\' c,
On matrix domains of triangles, Appl. Math. Comput. 189 (2)(2007),
1146-1163] we compute their $\beta$-duals, construct their basis and
characterize some matrix classes concerning with these spaces. We
also obtain estimates for the norms and the Hausdorff measures of
noncompactness of the bounded linear operators $L_A$ defined by the
infinity matrix $A\in(l_p(\Delta_u^\lambda), Y)$ where $Y$ is one of
the classic sequence spaces.
$C(\Delta_u^\lambda)$ have been recently introduced and studied. In
present paper, following the similar approach, we define a new
sequence spaces $l_p(\Delta_u^\lambda)$, $1\leq p \leq \infty$ and
by applying the general methods as in [E.Malkowsky, V. Rakocevi\' c,
On matrix domains of triangles, Appl. Math. Comput. 189 (2)(2007),
1146-1163] we compute their $\beta$-duals, construct their basis and
characterize some matrix classes concerning with these spaces. We
also obtain estimates for the norms and the Hausdorff measures of
noncompactness of the bounded linear operators $L_A$ defined by the
infinity matrix $A\in(l_p(\Delta_u^\lambda), Y)$ where $Y$ is one of
the classic sequence spaces.