Consistent classes of double summability methods

In 2000 Patterson proved that if a bounded double sequence is divergent then there are RH-regular matrix methods that sum it to various values. It is now natural to ask the following question. Is there a collection ΥΥ of RH-regular matrix methods which are consistent and such that every bounded double sequence is summable by at least one method in the collection? Similar to Goffman and Petersen’s presentation we will present a class of such a collection. In addition, it is clear from the presentation here that it is extremely difficult to find all such collections. However, we have extended this class to a countable collection of RH-regular matrix methods with bounded norm.