Recently, the invertibility of linear combinations of two idempotents has been studied by several authors. Let P and Q be idempotents in a Banach algebra. It was shown that the invertibility of P + Q is equivalent to that of aP + bQ for nonzero a, b with a + b 6= 0. In this note, we obtain a similar result for square zero operators and those operators satisfying x = dx for some scalar d. More g...
