Journal article

Publication year: 2014

Pages: 1059-1072

Journal: Filomat

Volume number: 28

Issue number: 5

ISSN: 0354-5180

Open access status: Bronze

DOI Link: https://doi.org/10.2298/FIL1405059M

Publisher: University of Nis

Abstract: 
We consider the sequence spaces s(alpha)(0)((B) over tilde), s(alpha)((c)) ((B) over tilde) and s(alpha)((B) over tilde) with their topological properties, and give the characterizations of the classes of matrix transformations from them into any of the spaces l(1), l(infinity), c(0) and c. We also establish some estimates for the norms of bounded linear operators defined by those matrix transformations. Moreover, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for a linear operator on the sets s(alpha)(0)((B) over tilde), s(alpha)((c))((B) over tilde) and s(alpha)((B) over tilde) to be compact. We also close a gap in the proof of the characterizations by various authors of matrix transformations on matrix domains.

Harvard Citation style: Malkowsky, E., Ozger, F. and Alotaibi, A. (2014) Some Notes on Matrix Mappings and their Hausdorff Measure of Noncompactness, Filomat, 28(5), pp. 1059-1072. https://doi.org/10.2298/FIL1405059M

APA Citation style: Malkowsky, E., Ozger, F., & Alotaibi, A. (2014). Some Notes on Matrix Mappings and their Hausdorff Measure of Noncompactness. Filomat. 28(5), 1059-1072. https://doi.org/10.2298/FIL1405059M