Minimal projections in bivariate function spaces (Q1063194)

(S,\(\Sigma\),\(\mu)\) and (T,\(\Theta\),\(\nu)\) are \(\sigma\)-finite, non-atomic measure spaces with S and T containing an infinite number of points. It is shown that the projection constants for \(L_ 1(S)+L_ 1(T)\) as a subspace of \(L_ p(S\times T)\) and for \(L_{\infty}(S)+L_{\infty}(T)\) as a subspace of \(L_{\infty}(S\times T)\) are both 3. An example of a minimal projection in both cases is exhibited.