Multilinear forms of Hilbert type and some other distinguished forms

Abstract

We give some new examples of bounded multilinear forms on th Hilbert spaces 2 and L2(0,∞). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m ≥ 3) on 2 which can be regarded as the multilinear analogue of the famous Hilbert matrix. We also determine the norm of the permanent on Kn, where K = R or C.