Entropy and Lorentz-Marcinkiewicz operator ideals (Q1106451)

The paper deals with ideals of operators for which the sequence of their entropy numbers \((e_ n(T))\) belongs to a Lorentz-Marcinkiewicz space \(\ell_{\phi,q}\), where \(\phi\) is a so-called function parameter. In the case \(\phi (t)=t^ p\) the classical Lorentz space \(\ell_{p,q}\) results. These ideals are compared with that obtained from the approximation, Gelfand and Kolmogorov numbers. The author further proves interpolation theorems and results about eigenvalue distributions.