On the linearity of some sets of sequences defined by $L_{p}$-functions and $L_{1}$-functions determining $ell_{1}$

摘要

In this paper, we discuss the linearity of a sequence space $Lambda_{p}(f)$, and the conditions such that $ell_{1} = Lambda_{1}(f)$ holds are characterized in term of the essential bounded variation of $fin L_{1}(mathbf{R})$, i.e. $ell_{1} = Lambda_{1}(f)$ if and only if $fin BV(mathbf{R})$.