## Matrix maps into the space of statistically convergent bounded sequences.(English)Zbl 0865.40001

Proc. Est. Acad. Sci., Phys. Math. 45, No. 2-3, 187-192 (1996); corrigendum ibid. 46, No. 1-2, 150 (1997).
A sequence space is any linear subspace of the vector space of all complex-valued sequences. For two sequence spaces $$X$$ and $$Y$$, denote by $$(X,Y)$$ the set of all doubly-infinite matrices $$A=(a_{nk})$$ such that, for each $$x\in X$$, $$A_nx\equiv\sum^\infty_{k=1}a_{nk}x_k$$ exists and the sequence $$(A_nx)\in Y$$. For such a matrix $$A$$, a sequence $$x$$ is $$A$$-statistically convergent to $$\ell$$ if, for every $$\varepsilon>0$$, $$\lim_{n\to\infty} \sum_{k\in V}a_{nk}=0$$, where $$V=\{k:|x_k-\ell|\geq\varepsilon\}$$. This paper characterizes the matrix class $$(X,Y_1)$$, where $$Y_1$$ is the space of all uniformly-bounded $$A$$-statistically convergent sequences and $$X$$ is a separable BK-space (i.e., a Banach sequence space with continuous coordinate functionals) with a countable fundamental set. The special cases where $$X$$ is the space of all convergent sequences and where $$X=\ell^p$$, $$p\geq 1$$, are considered.

### MSC:

 40C05 Matrix methods for summability 40A05 Convergence and divergence of series and sequences