Division by a holomorphic matrix in strictly pseudoconvex domains (Q1173829)

Let \(D\) be a bounded strictly pseudoconvex domain in \(\mathbb{C}^ n\) with \(C^ 2\)-boundary. The author proofs a matrix analogue of the known division theorem of Ovrelid [\textit{N. Ovrelid}, Generators of the maximal ideals of \(A(D)\), Pac. J. Math. 39, 219-223 (1971; Zbl 0231.46090)] for the algebra \(A(D)\) of the holomorphic functions in \(D\) and continuous in \(\overline D\). By the end he gives some results and problems in this area to other function algebras.