Chebyshev coefficients for \(L_ 1\)-preduals and for spaces with the extension property (Q757787)

The main results of the paper are: 1) a real normed space E is an \(L^ 1\)-predual iff \(\lambda_ f(E)=1/2\), and (2) if a real or complex normed space E is a \({\mathcal P}_{\ell}(K)\)-space then \(\lambda_ b(E)=\lambda_ b(K).\) Here, \(\lambda_ f(E)=\sup \{r(S)/\delta (S);\) \(S=\)0 finite part of \(E\}\) and \(\lambda_ b(E)=\sup \{r(S)/\delta (S);\) \(S=\) arbitrary part of \(E\}\) are Chebyshev coefficients and K is the ground field of E.