2021/05/27 by Andrei, Diana
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2105.13026
In the multicentric calculus one takes a polynomial with simple roots as a new global variable and replaces scalar functions φ by functions f taking values in Cd 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 Cd-valued continuous functions in such a way that the original functions φ appear as Gelfand transforms of f. In this paper we consider constructing a Banach algebra for functions from C2 into C^(d1 x d2) which then likewise leads to a functional calculus for commuting pairs of matrices.