Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1231.47029
Mursaleen, M.; Noman, Abdullah K.
Compactness of matrix operators on some new difference sequence spaces. (English)
[J] Linear Algebra Appl. 436, No. 1, 41-52 (2012). ISSN 0024-3795

The authors establish some identities or estimates for the Hausdorff measures of noncompactness of certain matrix operators on the difference sequence spaces $$ c_{o}^{\lambda }(\Delta) = \Big\{ ( x_{k}):\ \lim_{n\rightarrow \infty }\frac{1}{\lambda _{n}}\sum_{k=0}^{n} ( \lambda _{k}-\lambda _{k-1})(x_{k}-x_{k-1}) =0\Big\} $$ and $$ \ell_\infty^{\lambda }( \Delta) = \Big\{( x_{k}): \sup_{n}\left|\frac{1}{\lambda _{n}}\sum_{k=0}^{n}(\lambda _{k}-\lambda _{k-1})(x_{k}-x_{k-1})\right|<+\infty\Big\}\,,$$ where $\lambda =\left( \lambda _{k}\right)$ is a strictly increasing sequence of positive real numbers tending to infinity; see [{\it M. Mursaleen} and {\it A. K. Noman}, Math. Comput. Modelling 52, No.~ 3--4, 603--617 (2010; Zbl 1201.40003)]. Furthermore, they characterize some classes of compact operators on these spaces.
[Mohammad Sal Moslehian (Mashhad)]

MSC 2000:: *47B37 Operators on sequence spaces, etc.
47H08
46B45 Banach sequence spaces
46B50 Compactness in normed spaces
46B15 Summability and bases in normed spaces

Keywords: BK space; matrix transformation; compact operator; Hausdorff measure of noncompactness

Citations: Zbl 1201.40003

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]