Compact matrix operators between the spaces $m(\phi)$, $n(\phi)$ and $\ell_{p}$
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 1093-1103
https://doi.org/10.4134/BKMS.2011.48.5.1093
Printed September 1, 2011
Eberhard Malkowsky and Mohammad Mursaleen
Fatih University, Aligarh Muslim University
Abstract : We give the characterizations of the classes of matrix transformations $(m(\phi),\ell_{p})$, $(n(\phi),\ell_{p})$ ([5, Theorem 2]), $(\ell_{p},m(\phi))$ ([5, Theorem 1]) and $(\ell_{p},n(\phi))$ for $1\le p\le\infty$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations, and characterize the corresponding subclasses of compact matrix operators.
Keywords : sequence spaces, matrix transformations, compact operators, Hausdorff measure of noncompactness
MSC numbers : Primary 46B15; Secondary 46B45
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