Corrigendum to “Orbit closures in the enhanced nilpotent cone” [Adv. Math. 219 (1) (2008) 27–62]

In this note, we point out an error in the proof of Theorem 4.7 of [P.N. Achar, A. Henderson, Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (1) (2008) 27–62], a statement about the existence of affine pavings for fibres of a certain resolution of singularities of an enhanced nilpotent orbit closure. We also give independent proofs of later results that depend on that statement, so all other results of that paper remain valid.     

Erratum to “Separation of representations with quadratic overgroups” [Bull. Sci. Math. 135 (2) (2011) 141–165]

In the paper entitled “Separation of representations with quadratic overgroups”, we defined the notion of quadratic overgroups, and announced that the 6-dimensional nilpotent Lie algebra g6,20 admits such a quadratic overgroup. There is a mistake in the proof. The present Erratum explains that the proposed overgroup is only weakly quadratic, and g6,20 does not admit any natural quadratic overgroup.     

“Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1” [Ann. Sci. École Norm. Sup. (4) 34 (1) (2001) 1-61]

We correct in this note a mistake in [Delort, J.-M., Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1, Ann. Sci. École Norm. Sup. (4) 34 (1) (2001) 1-61], which has been indicated to us by H. Lindblad. The results of [Delort, J.-M., Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1, Ann. Sci. École Norm. Sup. (4) 34 (1) (2001) 1-61] still hold true if one increases the smoothness assumption made on the Cauchy data.     

Corrigendum to “The Dunkl intertwining operator” [J. Funct. Anal. 256 (8) (2009) 2697-2709]

In this note we correct the statement related to the regularity characterization of parameter functions and give some related new results.     

Addendum to “Contractive projections on Banach algebras” [J. Funct. Anal. 254 (10) (2008) 2513-2533]

The purpose of this addendum is to clarify two shortcomings in the paper of the title.     

S. G Mikhlin (1908 – 1990)

Our concern is to find a representation theorem for operators in B(c(X), c(Y)) where X and Y are Banach spaces with Y containing an isomorphic copy of c₀. Cass and Gao [1] obtained a representation theorem that always applies if Y does not contain an isomorphic copy of c₀. Maddox [3], Melvin - Melvin [4], and Robinson [5] consider operators in B(c(X), c(Y)) that are given by matrices. In this paper we show that Cass's and Gao's result in [1] can be extended, when Y contains an isomorphic copy of c₀, to certain operators that we call represent able. In addition, we show that when Y contains an isomorphic copy of co there are always operators that fall outside the scope of our representation theorem. Light is also cast on a theorem given in Maddox [3, Theorem 4.2] and [5, Theorem IV].