IJPAM: Volume 30, No. 3 (2006)

ON DOUBLE SEQUENCE SPACES $_{0}c_{2}^{P}(p),$ $_{0}c_{2}^{PB}(p)$ AND $\ell _{2}(p)$

Aysegül Gökhan$^1$, Rifat Çolak$^2$
$^{1,2}$Department of Mathematics
Firat University
Elazig, 23119, TURKEY
$^1$e-mail: agokhan1@firat.edu.tr
$^2$e-mail: rcolak@firat.edu.tr


Abstract.In this paper we introduce the double sequence spaces $_{0}c_{2}^{P}(p)$, $_{0}c_{2}^{PB}(p)$ and $\ell _{2}(p)$. We give some inclusion relations between these spaces. Furthermore we show that $_{0}c_{2}^{PB}(p)$ and $\ell _{2}(p)$ are complete paranormed spaces under some certain conditions. We also give the $\alpha -,\beta -$ and $\gamma -$ duals of the double sequence spaces $_{0}c_{2}^{PB}(p)$ and $\ell _{2}(p)$.

Received: June 5, 2006

AMS Subject Classification: 40A05, 40C05

Key Words and Phrases: double sequences, double series, double limit

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 3