On Summing Multipliers and Applications

A scalar sequence Ž i. is said to be a p-summing multiplier of a Banach space E, if Ý i 1 ixi p for all weakly p-summable sequences in E. We study some important properties of the space mpŽE. of all p-summing multipliers of E, consider applications to E-valued operators on the sequence space l p, and extend this work to general ‘‘summing multipliers.’’ The case p 1 shows close resemblance to the work of B. Marchena and C. Pi˜neiroŽQuaestiones Math., to appear., where the results originated from the authors’ interest in sequences in the ranges of vector measures