Geodesic
Characterization of weak type by the entropy distribution of r-nuclear operators
Studia Mathematica, Tome 107 (1993) no. 1, pp. 1-14 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm-107-1-1-14
Keywords: entropy numbers, r-nuclear operators, weak type 
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Martin Defant. Characterization of weak type by the entropy distribution of r-nuclear operators. Studia Mathematica, Tome 107 (1993) no. 1, pp. 1-14. doi: 10.4064/sm-107-1-1-14

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