An interesting result due to Dilworth et al. was that if we enlargegreedy sums by a constant factor \(\lambda > 1\) in the condition defining the greedyproperty, then we obtain an equivalence of the almost greedy property, a strictlyweaker property. Previously, the author showed that enlarging greedy sums by \(\lambda\) in the condition defining the partially greedy (PG) property also strictly weakensthe property. However, enlarging greedy sums in the definition of reverse partiallygreedy (RPG) bases by Dilworth and Khurana again gives RPG bases. The companionof PG and RPG bases suggests the existence of a characterization of RPGbases which, when greedy sums are enlarged, gives an analog of a result that holdsfor partially greedy bases. In this paper, we show that such a characterizationindeed exists, answering positively a question previously posed by the author.
