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We present a lower error bound for approximating linear multivariateoperators defined over Hilbert spaces in terms of the error bounds forappropriately constructed linear functionals as long as algorithms use functionvalues. Furthermore, some of these linear functionals have the same norm as thelinear operators. We then apply this error bound for linear (unweighted) tensorproducts. In this way we use negative tractability results known for linearfunctionals to conclude the same negative results for linear operators. Inparticular, we prove that $L_2$-multivariate approximation defined for standardSobolev space suffers the curse of dimensionality if function values are usedalthough the curse is not present if linear functionals are allowed.

Tractability of Multivariate Problems for Standard and Linear Information in the Worst Case Setting: Part I