On the Reciprocal of a K-Matrix*

Abstract

If the K-matrix A has a two-sided K_r-reciprocal A^-1, then A^-1 is itself a K-matrix.

For definitions and properties of K-and K_r-matrices, see Cooke [ 3 ] ; we follow the notation used in this book. The result is of interest, since the sets of K_r- and if-matrices are Banach algebras, the former containing the latter as a subalgebra.