Produits tensoriels d'espaces vectoriels topologiques
Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let and be Banach spaces such that is weakly compactly generated Asplund space and has the approximation property (respectively is weakly compactly generated Asplund space and has the approximation property). Suppose that and let . Then (respectively ) can be equivalently renormed so that any projection of onto has the sup-norm greater or equal to .
On the Lie ball w of Cn, n ≥ 3, we prove that for all p ∈ [1,∞), p ≠ 2, the Hardy space Hp(w) is an uncomplemented subspace of the Lebesgue space Lp(∂0w, dσ), where ∂0w denotes the Shilov boundary of w and dσ is a normalized invariant measure of ∂0w.