CHARACTERIZATION OF WEAK TYPE BY THE ENTROPY DISTRIBUTION OF R-NUCLEAR OPERATORS

The dual of a Banach space X is of weak type p if and only if the entr opy numbers of an r-nuclear operator with values in a Banach space of weak type q belong to the Lorentz sequence space l(s,r) with 1/s + 1/p + 1/q = 1 + 1/r (0 < r < 1, 1 less-than-or-equal-to p, q less-than-or -equal-to 2). It is enough to test this for Y = X. This extends resul ts of Carl, Konig and Kuhn.