Equivalence constants for matrix norms: A problem of Goldberg
The equivalence constants for the \(\ell^p\)-coefficient norms and \(\ell^q\)-operator norms \((1\leqslant p,q\leqslant\infty)\) of complex \(n\times m\) matrices are studied. The author establishes some new inequalities and provides a variety of known results for Goldberg's problem: Determine the best (least) constant \(c=c(m,n,p,q)\) such that \(|A|_p\leqslant c\|A\|_q\) for all \(m\times n\) matrices~\(A\). Here \(\|\cdot\|_p\) stands for the \(\ell^p\)-coefficient norm, and \(\|\cdot\|_q\) stands for the \(\ell^q\)-operator norm.
scientific article; zbMATH DE number 1421380
scientific article