Given any sequence a = (an)n1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n1 such that y=a = (yn=an)n1 2 E. In this paper, we use the spaces w1, w0 and w of strongly bounded, summable to zero and summable sequences, that are the sets of all sequences y such that ? n?1Pn k=1 jykj
n is bounded, tends to zero and such that y ? le 2 w0, for some scalar l, respectively, (cf. [24, 22]). These sets where used in the statistical convergence, (cf. [17, Chapter 4]). Then we deal with the solvability of each of the (SSIE) F
 E + F0x where E is a linear space of sequences, F = c0, c, `1, w0, w, or w1 and F0 = c0, c, or `1. For instance, the solvability of the (SSIE) w
 w0+s(c) x consists in determining the set of all sequences x = (xn)n1 2 U+ that satisfy the following statement. For every sequence y that satisfy the condition limn!1 n?1Pn k=1 jyk ? yk?1 ? lj = 0, there are two sequences u and v, with y = u+v such that limn!1 n?1Pn k=1 jukj = 0 and limn!1 (vn=xn) = L for some scalars l and L. These results extend those stated in [11, 12, 10].

BK polyomavirus (BKPyV) is still a real threat in the management of kidney transplantation. Immunosuppressive treatment disrupts the equilibrium between virus replication and immune response, and uncontrolled BKPyV replication leads to nephropathy (BKPyV nephropathy). The first evidence of BKPyV reactivation in transplant recipients is the detection of viral shedding in urine, which appears in 20% to 60% of patients, followed by BKPyV viremia in 10-20% of kidney transplant recipients. BKPyV nephropathy eventually occurs in 1-10% of this population, mainly within the first 2 years post-transplantation, causing graft loss in about half of those patients. Few data exist regarding the pediatric population and we focus on them. In this paper, we review the existing diagnostic methods, we summarize the evidences on the role of BKPyV humoral and cellular immunity in the modulation of the clinical course of BKPyV infection and as potential predictors of the outcome. We look at the known risk factors of BKPyV nephropathy in the immunosuppressed patient. Finally, we propose a sensible clinical attitude in order to screen and manage BKPyV infection in kidney transplant children.