A sum-shuffle formula for zeta values in Tate algebras

We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in \cite{PEL3}.This follows from an analog result for double twisted power sums, implying that an {\mathbb{F}\_p-vector space generated by multiple zeta values in Tate algebras is an {\mathbb{F}\_p-algebra.