DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B((r)over-tilde, (s)over-tilde) ON SOME MADDOX'S SPACES

作者：Ozger Faruk^*; Basar Feyzi

来源：Acta Mathematica Scientia, 2014, 34(2): 394-408.

• Matrix domain
• double sequential band matrices
• almost convergence
• paranormed spaces
• matrix transformations

The domain of generalized difference matrix B(r, s) in the classical spaces to 0, c, and cc was recently studied by Kirisci and Bagar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l(infinity)((B) over tilde, p), c((B) over tilde, p), and c(0)((B) over tilde, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l(infinity)((B) over tilde, p) c((B) over tilde, p) , and c(0)((B) over tilde, p) are computed and the bases of the spaces c((B) over tilde, p) and c(0)((B) over tilde, p) are constructed. The final section of this article is devoted to the characterization of the classes (lambda((B) over tilde, p) : mu) and (mu : lambda((B) over tilde, p)), where lambda epsilon {c, c(0), l(infinity)} and mu is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences.is obtained by means of a given lemma.

• 出版日期2014-3