  We present a lower error bound for approximating linear multivariate
operators defined over Hilbert spaces in terms of the error bounds for
appropriately constructed linear functionals as long as algorithms use function
values. Furthermore, some of these linear functionals have the same norm as the
linear operators. We then apply this error bound for linear (unweighted) tensor
products. In this way we use negative tractability results known for linear
functionals to conclude the same negative results for linear operators. In
particular, we prove that $L_2$-multivariate approximation defined for standard
Sobolev space suffers the curse of dimensionality if function values are used
although the curse is not present if linear functionals are allowed.
