Matrix Transformations Involving Generalized Almost Convergent Sequences

摘要

In [7] Maddox generalized the spaces c(0), c, (1), by adding powers p(k) (k N) in the definitions of the spaces to the terms of the elements of the sequences (x(k)). Using the ideas of Maddox, Nanda [13] defined generalizations f(p) and f(0)(p) of the spaces of all almost convergent sequences f and of all sequences f(0) almost convergent to 0. In [13] and [14] he characterized some classes of matrix transformations involving theses spaces and Maddox's sequence spaces. We have discovered that almost all results in [13] and [14] are faulty. In this paper we give corresponding counterexamples and prove the correct results. Moreover we prove them in more general settings.