  Suppose B is the unital algebra consisting of the algebraic product of full
matrix algebras over an index set X. A bijection is set up between the
equivalence classes of irreducible representations of B as operators on a
Banach space and the sigma-complete ultrafilters on X, Theorem 1. Therefore, if
X has less than measurable cardinality (e.g. accessible), the equivalence
classes of the irreducible representations of B are labeled by points of X, and
all representations of B are described, Theorem 3.
