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In the paper, we prove two theorems on summability, , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.
In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "" with arbitrary linear regular summability methods we consider the notion of a generalized continuity (-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.
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