Séminaires : Séminaire d'Analyse Fonctionnelle

We study the asymptotic behaviour of large symmetric tensor powers of finitely dimensional normed vector spaces. More precisely, contrary to full tensor powers, we show that the distortion between the injective and projective tensor norms grows subexponentially on symmetric tensor powers of a fixed finitely dimensional complex normed vector space. We will then apply this to give a classification result for graded commutative normed algebras. If time permits, we discuss the motivations for these questions arising from complex and algebraic geometry.