zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Compactness of matrix operators on some new difference sequence spaces. (English) Zbl 1231.47029
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.

47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
46B45Banach sequence spaces
46B50Compactness in Banach (or normed) spaces
46B15Summability and bases in normed spaces
Full Text: DOI
[1] Başar, F.; Malkowsky, E.; Altay, B.: Matrix transformations on the matrix domains of triangles in the spaces of strongly C1-summable and bounded sequences, Publ. math. Debrecen 73, No. 1 -- 2, 193-213 (2008) · Zbl 1164.46003
[2] Djolović, I.: Compact operators on the spaces $a0r(\Delta )$ and $acr(\Delta )$, J. math. Anal. appl. 318, No. 2, 658-666 (2006) · Zbl 1099.47021 · doi:10.1016/j.jmaa.2005.05.085
[3] Djolović, I.; Malkowsky, E.: A note on compact operators on matrix domains, J. math. Anal. appl. 340, No. 1, 291-303 (2008) · Zbl 1147.47002 · doi:10.1016/j.jmaa.2007.08.021
[4] Djolović, I.; Malkowsky, E.: Matrix transformations and compact operators on some new mth-order difference sequences, Appl. math. Comput. 198, No. 2, 700-714 (2008) · Zbl 1148.46007 · doi:10.1016/j.amc.2007.09.008
[5] Djolović, I.; Malkowsky, E.: A note on Fredholm operators on (c0)T, Appl. math. Lett. 22, No. 11, 1734-1739 (2009) · Zbl 1188.47012 · doi:10.1016/j.aml.2009.06.012
[6] Malkowsky, E.: Compact matrix operators between some BK spaces, Modern methods of analysis and its applications, 86-120 (2010)
[7] E. Malkowsky, V. Rakočević, An introduction into the theory of sequence spaces and measures of noncompactness, Zbornik radova 9 (17), Mat. institut SANU (Beograd), 2000, pp. 143 -- 234. · Zbl 0996.46006
[8] Malkowsky, E.; Rakočević, V.: On matrix domains of triangles, Appl. math. Comput. 189, No. 2, 1146-1163 (2007) · Zbl 1132.46011 · doi:10.1016/j.amc.2006.12.024
[9] Malkowsky, E.; Rakočević, V.; Živković, S.: Matrix transformations between the sequence spaces $w0p(\Lambda ), v0p(\Lambda ), c0p(\Lambda )$ (1<p$<\infty $) and certain BK spaces, Appl. math. Comput. 147, No. 2, 377-396 (2004) · Zbl 1035.46001 · doi:10.1016/S0096-3003(02)00674-4
[10] Mursaleen, M.; Noman, A. K.: On some new difference sequence spaces of non-absolute type, Math. comput. Modelling 52, No. 3 -- 4, 603-617 (2010) · Zbl 1201.40003 · doi:10.1016/j.mcm.2010.04.006
[11] Mursaleen, M.; Noman, A. K.: Compactness by the Hausdorff measure of noncompactness, Nonlinear anal.: TMA 73, No. 8, 2541-2557 (2010) · Zbl 1211.47061 · doi:10.1016/j.na.2010.06.030
[12] Stieglitz, M.; Tietz, H.: Matrixtransformationen von folgenräumen eine ergebnisübersicht, Math. Z. 154, 1-16 (1977) · Zbl 0331.40005 · doi:10.1007/BF01215107