Displaying similar documents to “Entropy numbers of r-nuclear operators in Banach spaces of type q”

Characterization of weak type by the entropy distribution of r-nuclear operators

Martin Defant, Marius Junge (1993)

Studia Mathematica

Similarity:

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.