Local entropy moduli and eigenvalues of operators in Banach spaces (Q1085412)

Local entropy moduli of bounded linear operators between Banach spaces are introduced as a generalization of the well-known entropy numbers and their moduli which measure the ''degree of compactness'' of such operators. Relations between local entropy moduli, various s-numbers and eigenvalues are given, with the particular cases of absolutely summing operators and of inclusion and diagonal operators between \(\ell_ p\)-spaces treated in detail. In addition, an application of these ideas to the estimation of the eigenvalues of certain integral operators between \(L_ p\)-spaces is given.