Abstract
It is well known that every bounded sequence is limitable by some regular matrix. Our object is to define some classes of regular matrices such that every bounded sequence is limitable by some member of each class. We consider matrices and sequences of complex numbers and write I for the unit interval [0, 11. N for the set of natural numbers. For each (I E I, we denote by Q(a) the class of regular matrices A = (a,,) such that a,,,,, > 0 for all m, n E N and, in addition, for each m E N, there is 11 E N such that a,,,,, = c( and also for each n E N, there is m E N such that a mn = u. The following results will be established Iirst.
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