ABSOLUTELY SUMMING MULTIPLIERS AND TOPOLOGIES ON L(E,F)

Abstract

We introduce the concepts of weak Z-topology and ultra-weak Z-topology on the space L(E,F) of continuous linear functions from E into F, where E and F are locally convex spaces. The dual spaces of L(E,F) under these topologies are characterized. The ultra-weak Z-topology generalizes the well known ultra-weak topology on the Banach algebra B(H). Alternative characterizations of the above mentioned dual spaces of L(E, F) are obtained in the Banach space setting. In this case some results on multiplier spaces of Banach spaces are important. We present a partial answer to the question of characterizing absolutely summing multiplier spaces in terms of l^p spaces.