Finite dimensional semisimple \(Q\)-algebras
Let \(A\) be a uniform algebra on a compact Hausdorff space \(X\) and \(I\) be a closed ideal of \(A\). Then \(A/I\) is a commutative Banach algebra with unit. Here a Banach algebra \(B\) is called a \(Q\)-algebra if it is isometrically isomorphic to \(A/I\). Finite \(n\)-dimensional semisimple \(Q\)-algebras on a finite \(n\)-dimensional Hilbert space are studied in the present paper. In particular, a 3-dimensional \(Q\)-algebra of a disc algebra on a 3-dimensional Hilbert space is described. The studies are related to the Pick interpolation problem for a uniform algebra.
finite dimensional semisimple \(Q\)-algebras
scientific article; zbMATH DE number 5083611