Sum of sequence spaces and matrix transformations

Summary We are interested in the study of the sum ]]>]]>]]>]]>]]>]]>]]>]]>]]>]]>]]>E+F$ and the product $E*F$, when $E$ and $F$ are of the form $s_{xi}$, or $s_{xi}^{circ}$, or $s_{xi}^{(c)}$. Then we deal with the identities $(E+F) (Delta^{q}) eg E$ and $(E+F) (Delta^{q}) eg F$. Finally we consider matrix transformations in the previous sets and study the identities $big((E^{p_{1}}+F^{p_{2}}) (Delta^{q}),s_{mu}big) eg S_{alpha^{p_{1}}pl beta^{p_{2}},mu}$ and $big(E+F(Delta^{q}),s_{gamma}big) eg S_{beta,gamma}$.