Interpolation of Ces{\`a}ro sequence and function spaces

The interpolation property of Ces{`a}ro sequence and function spaces is investigated. It is shown that $Ce{s}_p(I)$ is an interpolation space between $Ce{s}_{p_0}(I)$ and $Ce{s}_{p_1}(I)$ for $1<p_0<p_1\le \mathrm{\infty }$ and $1/p = (1

• \theta)/p_0 + \theta /p_1$with$0 < \theta < 1$,where$I = [0, \infty)$or$[0, 1]$. The same result is true for Ces{`a}ro sequence spaces. On the other hand, $Ce{s}_p[0,1]$ is not an interpolation space between $Ce{s}_1[0,1]$ and $Ce{s}_{\mathrm{\infty }}[0,1]$.