Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1072.46007
Aydin, Cafer; Başar, Feyz i
Some new difference sequence spaces. (English)
[J] Appl. Math. Comput. 157, No. 3, 677-693 (2004). ISSN 0096-3003

Summary: The difference sequence spaces $\ell_\infty(\Delta)$, $c (\Delta)$ and $c_0(\Delta)$ were studied by {\it H. Kizmaz} [Can. Math. Bull. 24, 169--176 (1981; Zbl 0454.46010)]. The sequence spaces $a^r_0$ and $a^r_c$ have been recently defined and examined by {\it C. Aydin} and {\it F. Basar} [Hokkaido Math. J. 33, No. 2, 383--398 (2004; Zbl 1085.46002)]. The main purpose of the present paper is to introduce the spaces $a^r_0(\Delta)$ and $a^r_c(\Delta)$ of difference sequences. Moreover, it is proven that the spaces $a^r_0 (\Delta)$ and $a^r_c(\Delta)$ are BK-spaces including the spaces $c_0$ and $c$, and some inclusion relations are given. It is also proven that the sequence space $a^r_0$ has the AD property while the space $a^r_0 (\Delta)$ does not. Furthermore, a basis and the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces $a^r_0 (\Delta)$ and $a^r_c(\Delta)$ are determined. The last section of the paper is devoted to characterizations of the matrix classes $(a^r_c (\Delta):\ell_p)$ and $(a^r_c(\Delta):c)$, and the characterizations of some other matrix classes are obtained by means of a given basic lemma, where $1\le p\le\infty$.

MSC 2000:: *46A45 Sequence spaces

Keywords: difference sequence spaces; AD property; Schauder basis; $\alpha$-, $\beta$- and $\gamma$-duals; matrix mappings

Citations: Zbl 0454.46010; Zbl 1085.46002

Cited in: Zbl 1171.40002 Zbl 1099.47021

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