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Applications of measure of noncompactness in matrix operators on some sequence spaces. (English) Zbl 1237.47039
Summary: We determine the conditions for some matrix transformations from $n(\phi)$, where the sequence space $n(\phi)$, which is related to the $\ell_p$ spaces, was introduced by {\it W. L. C. Sargent} [J. Lond. Math. Soc. 35, 161--171 (1960; Zbl 0090.03703)]. We also obtain estimates for the norms of the bounded linear operators defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

##### MSC:
 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47H08 Measures of noncompactness and condensing mappings, $K$-set contractions, etc. 46A45 Sequence spaces
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##### References:
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