Annals of Functional Analysis

Domain of the triple band matrix on some Maddox's spaces

Feyzi Başar and Ahmet Faruk Çakmak

Full-text: Open access

Abstract

‎The sequence spaces $\ell_\infty(p)$‎, ‎$c(p)$ and $c_0(p)$ were‎ ‎introduced and studied by Maddox [Proc‎. ‎Cambridge Philos‎. ‎Soc‎. ‎64‎ ‎(1968)‎, ‎335-340]‎. ‎In the present paper‎, ‎we introduce the sequence‎ ‎spaces $\ell_\infty(B,p)$‎, ‎$c(B,p)$ and $c_0(B,p)$ of non-absolute‎ ‎type which are derived by the triple band matrix $B(r,s,t)$ and is‎ ‎proved that the spaces $\ell_\infty(B,p)$‎, ‎$c(B,p)$ and $c_0(B,p)$‎ ‎are paranorm isomorphic to the spaces $\ell_\infty(p)$‎, ‎$c(p)$ and‎ ‎$c_0(p)$; respectively‎. ‎Besides this‎, ‎the $\alpha$-‎, ‎$\beta$‎- ‎and‎ ‎$\gamma$-duals of the spaces $\ell_\infty(B,p)$‎, ‎$c(B,p)$ and‎ ‎$c_0(B,p)$ are computed and the bases of the spaces $c(B,p)$ and‎ ‎$c_0(B,p)$ are constructed‎. ‎Finally‎, ‎the matrix mappings from the‎ ‎sequence spaces $\lambda(B,p)$ to a given sequence space $\mu$ and‎ ‎from the sequence space $\mu$ to the sequence space $\lambda(B,p)$‎ ‎are characterized‎, ‎where $\lambda\in\{\ell_\infty,c,c_0\}$‎.

Article information

Source
Ann. Funct. Anal., Volume 3, Number 1 (2012), 32-48.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900022

Digital Object Identifier
doi:10.15352/afa/1399900022

Mathematical Reviews number (MathSciNet)
MR2903266

Zentralblatt MATH identifier
1262.46003

Subjects
Primary: 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]
Secondary: 40C05: Matrix methods

Keywords
Paranormed sequence space ‎matrix domain $f$- $\beta$‎- ‎and $\gamma$-duals ‎triple band matrix ‎AD property and matrix transformations

Citation

Başar, Feyzi; Çakmak, Ahmet Faruk. Domain of the triple band matrix on some Maddox's spaces. Ann. Funct. Anal. 3 (2012), no. 1, 32--48. doi:10.15352/afa/1399900022. https://projecteuclid.org/euclid.afa/1399900022


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