In the paper (Vietnam J. Math. 42: 153–157, 2014) (cf. also the earlier appeared and more general paper (Kathmandu Univ. J. Sci. Eng. Technol. 8: 89–92, 2012)), Ganie and Sheikh characterized matrices A = (ank) ∈ (bv(p), Y) in terms of the matrix coefficients ank, where Y ∈ { a c ∞ , a c , a c 0 } (the space of sequences being almost bounded, almost convergent, and almost convergent to 0, respectively). In this publication, we pursue two aims: The first one is to give an example showing that none of the results in (Vietnam J. Math. 42: 153–157, 2014) (and thus none of the Theorems 2.3 and 2.4 and Corallary 2.5 in (Kathmandu Univ. J. Sci. Eng. Technol. 8, 89–92, 2012)) is correct in general and to correct and extend these results. The second one is to apply the reduction method presented in (J. Anal. 9: 149–181, 2001). In this way, we get easily the (corrected) results of Ganie and Sheikh (cf. Remark 7) and many other theorems of Toeplitz–Silverman type (cf. Sections 5 and 6) by reduction to known theorems of Toeplitz–Silverman type. So it is not necessary to prove all the results completely anew, as Ganie and Sheikh tried.