Multilinear forms of Hilbert type and some other distinguished forms
We give some new examples of bounded multilinear forms on the Hilbert spaces l(2) and L-2(0, infinity). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m >= 3) on l(2) which can be regarded as the multilinear analogue of the famous Hilbert matrix. We also determine the norm of the permanent on K-n, where K = R or C.