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Zbl 1237.47039
Mursaleen, M.; Latif, A.
(Mursaleen, Mohammad;)
Applications of measure of noncompactness in matrix operators on some sequence spaces. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 378250, 10 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

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 2000:: *47B37 Operators on sequence spaces, etc.
47H08
46A45 Sequence spaces

Citations: Zbl 0090.03703

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Zentralblatt MATH Berlin [Germany]