  It is well-known that in Banach spaces with finite cotype, the $R$-bounded
and $\gamma$-bounded families of operators coincide. If in addition $X$ is a
Banach lattice, then these notions can be expressed as square function
estimates. It is also clear that $R$-boundedness implies $\gamma$-boundedness.
In this note we show that all other possible inclusions fail. Furthermore, we
will prove that $R$-boundedness is stable under taking adjoints if and only if
the underlying space is $K$-convex.
