group amenability for direct sum and tensor product of von neumann algebras

For a family of von neumann algebras $left(m_{i}ight)_{i in i}$ and a‎ locally compact group $g$‎, ‎we consider the concept of $g$-amenability of direct sum‎ ‎$igoplus_{i} m_{i}$‎. ‎we prove that‎ if $igoplus_{i} m_{i}$ is g-amenable‎, ‎then every $m_i$ is g-amenable‎. but if one of the elements of the family $left(m_{i}ight)_{i in i}$ is $g$-amenable‎, ‎then‎‎$igoplus_{i} m_{i}$ is $g$-amenable‎. ‎finally‎, ‎for two von neumann algebras $m$ and $n$‎, ‎we show‎ ‎that the von neumann algebraic tensor product of $m$ and $n$ is $gimes h$-amenable if and only if‎ ‎$m$ is $g$-amenable and $n$ is $h$ amenable.