IJPAM: Volume 35, No. 3 (2007)


W. Shatanawi$^1$, M. Khandaqji$^2$, A. Al-Rawashdeh$^3$
$^{1,2}$Department of Mathematics
The Hashemite University
P.O. Box 150459, Zarqa, 13115, JORDAN
$^{1}$email: swasfi@hu.edu.jo
$^{2}$email: mkhan@hu.edu.jo
$^{3}$Department of Mathematics
Jordan University of Science and Technology
e-mail: rahmed@just.edu.jo

Abstract.In the present paper, we show that a bounded linear map $T$ from a Hilbert space $H$ into a reflexive Banach space $F$ is an absolutely 2-summing map iff it is a 2-quasi-nuclear map. Also, for a nuclear $G_\infty$-spaces $\lambda(P)$ and $\lambda(Q)$, we show that a bounded linear map $T$ between normed spaces is 2-quasi- $\lambda(P)*\lambda(Q)$ iff it is quasi- $\lambda(P)*\lambda(Q)$-nuclear. Then we introduce an example to show that the nuclearity of $\lambda(P)$ and $\lambda(Q)$ are necessary.

Received: November 21, 2006

AMS Subject Classification: 46A45, 47B10, 47L20

Key Words and Phrases: nuclear maps, absolutely 2-summing maps, quasi $\lambda$-nuclear maps

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 3