On the Concept of Multiple Summing Multilinear Operators
Awadh Bihari Yadav
*
Department of Mathematics, C. M. science College, Darbhanga, Bihar, India.
*Author to whom correspondence should be addressed.
Abstract
Let \(\Sigma\) be a \(\sigma\)-algebra of subsets of a completely regular Hausdorff space \(X\) and \(E\) be a Banach space. For \(1 \leq p, q<\infty\), we characterize multiple ( \(p, q\) )- summing multilinear operators on the product of Banach spaces B \((\Sigma\), E) of all E-valued totally measurable functions on a set \(X\), equipped with the supremum norms in terms of their representing operator-valued polymeasures. As a consequence, we obtain some novel characterization of ( \(p, q\) )-summing a multilinear operator on \(B(\Sigma, E)\) in terms of their representing measures and ideal of multilinear mappings.
Keywords: Absolutely summing operator, operator valued measures, multilinear operator, operator ideals