Are unbounded linear operators computable on the average for Gaussian measures? (Q945917)

The author discusses the problem whether every linear operator \(S: \subseteq X \rightarrow Y\) is computable on the average w.r.t.~a Gaussian measure on \(X\) [see also \textit{J. F. Traub} and \textit{A. G. Werschulz}, Complexity and information, Lezioni Lincee. Cambridge: Cambridge Univ. Press. (1998; Zbl 0917.68094)]. Several interpretations of this question within the framework of type-2 theory of effectivity are given. Furthermore, two equivalent representations for the class of all Gaussian measures on \(\ell^2\) are given.