IJPAM: Volume 75, No. 2 (2012)

WEAK IDEAL CONVERGENCE IN $l_p$ SPACES

Vinod K. Bhardwaj$^1$, Anju Rani$^2$
$^{1,2}$Department of Mathematics
Kurukshetra University
Kurukshtera, 136119, INDIA


Abstract. In this paper, we see that how weak ideal convergence `looks like' in $l_{p} $ spaces. We extend the recently introduced concept of weak$^*$ statistical convergence to have a new concept of weak$^*$ ideal convergence. We give the necessary and sufficient conditions for a sequence of bounded linear functionals on a Banach space to be weak$^*$ ideal convergent.

Received: December 10, 2011

AMS Subject Classification: 40A05

Key Words and Phrases: ideal convergence, weak ideal convergence, weak$^*$ ideal convergence

Download paper from here.



Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 2