Tensor products of C(X)-algebras over C(X)

Etienne Blanchard (1)

1 IMJ - Institut de Mathématiques de Jussieu

Given a Hausdorff compact space $X$, we study the \mbox{${\rm C}^*$}-(semi)-norms on the algebraic tensor product $A\odot_{C(X)} B$ of two $C(X)$-algebras $A$ and $B$ over $C(X)$. In particular, if one of the two $C(X)$-algebras defines a continuous field of \mbox{${\rm C}^*$}-algebras over $X$, there exist minimal and maximal \mbox{${\rm C}^*$}-norms on $A\odot_{C(X)} B$ but there does not exist any \mbox{${\rm C}^*$}-norm on $A\odot_{C(X)} B$ in general.

Mots clés: C*-algebra continuous field; Tensor product

Domaines: Algèbres d'opérateurs [math.OA]

Etienne Blanchard. Tensor products of C(X)-algebras over C(X). Asterisque, 1995, 232, pp.81--92. ⟨hal-00922902v2⟩