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1 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1 1998

1 Aasma A.

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Matrix transformations of [lambda]-summability fields of [lambda]-reversible and [lambda]-perfect methods

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Aasma A.

tom [Z] 38

1-20

In this paper we shall consider the summability with speed. Let [lambda] and m be two monotonically increasing sequences (i.e.speeds) and B be a triangular matrix. In [4] there were found the necessary and sufficient conditions for a matrix M to be transformation of the [lambda]-boundedness field of normal matrix A into the u-boundedness field of B. Now we shall continue the research, started in [4]. More precisely, we shall prove two theorems which give the necessary and sufficient conditions for a matrix M to be transformation of the [lambda]-summability field of [lambda]-reversible matrix A into the u-summability or u-boundedness field of B ((Theorems 1 and 2). Also we shall consider the case, when A is a [lambda]-perfect matrix (Theorem 3). For application we shall consider the special cases when A or A and B booth are Cesaro or Riesz methods. We note that notions [lambda]-reversibility and [lambda]-perfectness were introduced by G.Kangro in [10].