INTEGRATED RATE SPACE ∫ ℓπ

This paper deals with the BK-AK property of the integrated rate space ${\int}{\ell}_{\pi}$. Importance of ${\delta}^{(k)}$ in this content is pointed out. We investigate a determining set for the integrated rate space ${\int}{\ell}_{\pi}$. The set of all infinite matrices transforming ${\int}{\ell}_{\pi}$, into BK-AK space Y is denoted $({\int}{\ell}_{\pi}:\;Y)$. We characterize the classes $({\int}{\ell}_{\pi}:\;Y)$. When $Y={\ell}_{\infty},\;c_0,\;c,\;{\ell}^p,\;bv,\;bv_0,\;bs,\;cs,\;{\ell}_p,\;{\ell}_{\pi}$. In summary we have the following table: