  In the multicentric calculus one takes a polynomial with simple roots as a
new global variable and replaces scalar functions {\varphi} by functions f
taking values in C^d with d the degree of the polynomial leading to an
efficient holomorphic functional calculus for bounded operators. This calculus
was extended for non-holomorphic functions, so that if A is not diagonalizable
one can find a p such that p(A) is diagonalizable and apply the calculus to all
matrices. This was done in [7] by creating a Banach algebra for C^d-valued
continuous functions in such a way that the original functions {\varphi} appear
as Gelfand transforms of f. In this paper we consider constructing a Banach
algebra for functions from C^2 into C^(d_1 x d_2) which then likewise leads to
a functional calculus for commuting pairs of matrices.
