Minimal projections in tensor-product spaces (Q5896372)

The relative projection constant of a subspace V of a Banach space X is the number \(\lambda(V,X)=\inf \{\| p\|:P\) projects X onto \(V\}\). This paper deals with projection of subspaces of tensor product spaces. Most often the following situation is considered (where the norm used is the injective tensor product norm): \(X=C(S)\otimes C(T)=C(S\times T); V=G\otimes C(T)+C(S)\otimes H\) where G and H are subspaces of C(S) and C(T) respectively. With these notations, the main result of the paper is the following. Theorem: If S and T are infinite compact Hausdorff spaces, G and H are finite dimensional and contain the constants then \(\lambda\) (V,X)\(\geq 1\). The above theorem extends a previous result by \textit{G. J. Jameson} and \textit{A. Pinkus} [ibid. 37, 182-195 (1983; Zbl 0508.41026)].