Journal article

Publication year: 2007

Pages: 521-532

Journal: Acta Mathematica Sinica, English Series

Volume number: 23

Issue number: 3

ISSN: 1439-8516

DOI Link: https://doi.org/10.1007/s10114-005-0719-x

Publisher: Springer

Abstract: 
Let p = (p(k))(k=0)(infinity) be a bounded sequence of positive reals, m is an element of N and u be s sequence of nonzero terms. If x = (x(k))(k=0)(infinity) is any sequence of complex numbers we write Delta((m)) x for the sequence of the m-th order differences of x and Delta((m))(u) X = {x = (x)(k=0)(infinity) : u Delta(m) x is an element of X} for any set X of sequences. We determine the alpha-, beta- and gamma- duals of the sets Delta((m))(u) X for X = c(0)(p), c(p), l(infinity)(p) and characterize some matrix transformations between these spaces Delta(m) X.

Harvard Citation style: Malkowsky, E., Mursaleen, M. and Suantai, S. (2007) The dual spaces of sets of difference sequences of order m and matrix transformations, Acta Mathematica Sinica, English Series, 23(3), pp. 521-532. https://doi.org/10.1007/s10114-005-0719-x

APA Citation style: Malkowsky, E., Mursaleen, M., & Suantai, S. (2007). The dual spaces of sets of difference sequences of order m and matrix transformations. Acta Mathematica Sinica, English Series. 23(3), 521-532. https://doi.org/10.1007/s10114-005-0719-x