Let \(X\) be a Banach space. An operator \(T\in B(X)\) is said to be subscalar (in fact, \(\infty\)-subscalar) if it is similar to the restriction of a generalized scalar operator to one of its closed invariant subspaces [J. Eschmeier and M. Putinar, Indiana Univ. Math. J. 37, 325–348 (1988; Zbl 0674.47020)]. The authors prove that if \(R\), \(S\in B(X)\) are injective, then \(RS\) is subscalar if and oly if \(SR\) is subscalar. As corollaries, the authors extend M. Putinar’s theorem [J. Operator Theory 12, 385–395 (1984; Zbl 0573.47016)] to \(p\)-hyponormal operators, log-hyponormal operators, and \(w\)-hyponormal operators \(T\) with \(\ker T\subset\ker T^*\). In fact, they show that \(p\)-hyponormal operators, log-hyponormal operators, and \(w\)-hyponormal operators \(T\) with \(\ker T\subset\ker T^*\) are subscalar.