© Hindawi Publishing Corp. ON MATRIX TRANSFORMATIONS CONCERNING THE NAKANO VECTOR-VALUED SEQUENCE SPACE

Abstract. We give the matrix characterizations from Nakano vector-valued sequence space (X,p) and Fr (X,p) into the sequence spaces Er, ∞, ∞(q), bs, and cs, where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk> 1 for all k∈N and r ≥ 0. 2000 Mathematics Subject Classification. 46A45. 1. Introduction. Let (X, ‖ · ‖) be a Banach space, r ≥ 0 and p = (pk) a bounded sequence of positive real numbers. We write x = (xk) with xk in X for all k ∈N. The X-valued sequence spaces c0(X,p), c(X,p), ∞(X,p), (X,p), Er (X,p), Fr (X,p), and ∞(X,p) are defined a