Globally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change‎, ‎I‎ : ‎Iwasawa algebras and a base change map

This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2‎, ‎mathbb{Z}_p)$‎. ‎It then describes a natural base change map between the Iwasawa algebras or more correctly‎, ‎as it turns out‎, ‎between the global distribution algebras on the associated rigid-analytic spaces‎. ‎In a forthcoming paper this will be applied to $p$-adic representation theory‎.