Bounded index and four dimensional summability methods

Fatih Nuray

In this paper, we present necessary and sufficient conditions on four dimensional matrix transformations that preserve entireness, bounded index and absolute convergence of double sequences. We begin this analysis with the following observation: The four dimensional Taylor matrix $T$ transforms the set of double sequences of bounded index into itself. After this observation, we present general characterizations for four dimensional RH-regular matrix transformations for the space of entire, bounded index, and absolutely summable double sequences.