For a locally convex space E we prove that the space of n-symmetric tensors is complemented in the space of (n+1)-symmetric tensors endowed with the projective topology. Applications and related results are also given.
Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].
The problem of finding complemented copies of l in another space is a classical problem in Functional Analysis and has been studied from different points of view in the literature. Here we pay attention to complementation of l in an n-fold tensor product of l spaces because we were lead to that result in the study of Grothendieck's Problème des topologies as we shall comment later.
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