GAPS BETWEEN CLASSES OF MATRIX MONOTONE FUNCTIONS.

The class $P_n(I)$ of matrix monotone functions of order $n$</formtex>, defined on an open interval $I$</formtex>, is considered in this paper. Explicit examples are given to prove that if $I$</formtex> is different from the whole real line, then $P_{n+1}(I)$</formtex> is a proper subset of $P_n(I)$</formtex> for each natural number $n$</formtex>. The subhomogeneous C*-algebras are then characterized in terms of matrix monotone functions. [ABSTRACT FROM AUTHOR]