Comments on "Is the Frobenius Matrix Norm Induced?" and reply

In "Is the Frobenius matrix norm induced?", the authors ask whether the Frobenius and the H/sup 2/ norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the H/sup 2/ norm may not be induced. In this paper, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the H/sup 2/ norm is in fact induced on a particular matrix-valued L/sup (infinity)/ space. A reply is provided to the comments.