Characterization of weak type by the entropy distribution of r-nuclear operators
Volume 107 / 1993
Studia Mathematica 107 (1993), 1-14
DOI: 10.4064/sm-107-1-1-14
Abstract
The dual of a Banach space X is of weak type p if and only if the entropy 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 ≤ p, q ≤ 2). It is enough to test this for Y = X*. This extends results of Carl, König and Kühn.
