Regular methods of summability for direct sums of Banach spaces

Regular matrix methods of summability and real interpolation

“…The Cauchy criterion provided by Lemma 3.1 leads to the following general result proved in [6]. In particular, this result can be applied to spaces l p (ξ, X) used in the discrete interpolation methods.…”

“…The key result which we use in the proof of our theorem depends on the following lemma proved in [6] with the use of the Galvin-Prikry theorem [4]. Lemma 3.1.…”

“…Instead of spreading models, we refer more directly to the Galvin-Prikry theorem on Ramsey sets [4]. We apply a result concerning behavior of regular summation for direct sums of Banach spaces recently proved in [6]. We obtain a general result for all positive matrix methods of summability which include the lower triangular matrix of arithmetic means.…”