Annals of Functional Analysis

Some $m$th-order Difference Sequence Spaces of Generalized Means and Compact Operators

Amit Maji, Atanu Manna, and P. D. Srivastava

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Abstract

In this paper, new sequence spaces $X(r, s, t ;\Delta^{(m)})$ for $X\in \{l_\infty, c,$ $c_0\}$ defined by using generalized means and difference operator of order $m$ are introduced. It is shown that these spaces are complete normed linear spaces and the spaces $c_0(r, s, t ;\Delta^{(m)})$, $c(r, s, t ;\Delta^{(m)})$ have Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t ;\Delta^{(m)})$ to $X$. Finally, some classes of compact operators on the spaces $c_0(r, s, t ;\Delta^{(m)})$ and $l_{\infty}(r, s, t ;\Delta^{(m)})$ are characterized by using the Hausdorff measure of .

Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 170-192.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1419001458

Digital Object Identifier
doi:10.15352/afa/06-1-13

Mathematical Reviews number (MathSciNet)
MR3297795

Zentralblatt MATH identifier
1339.46005

Subjects
Primary: 46A45
Secondary: 46B15: Summability and bases [See also 46A35] 46B50: Compactness in Banach (or normed) spaces

Keywords
Difference operator generalized means matrix transformation Hausdorff measure of compact operators

Citation

Maji, Amit; Manna, Atanu; Srivastava, P. D. Some $m$th-order Difference Sequence Spaces of Generalized Means and Compact Operators. Ann. Funct. Anal. 6 (2015), no. 1, 170--192. doi:10.15352/afa/06-1-13. https://projecteuclid.org/euclid.afa/1419001458


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