Some multiple summing operators defined by the determinant of a matrix

Abstract

We give some new examples of multilinear Hilbert-Schmidt and multiple summing operators, involving the determinant of a n × n -square matrix of scalars. We also determine the exact value of the Hilbert-Schmidt and multiple summing norms  and we show that both of them are related to the permanent of a certain matrix.

Keywords: Multiple p-summing operators, Hilbert-Schmidt operators, permanents

Quaestiones Mathematicae 35(2012), 1–9