Entropy and Lorentz-Marcinkiewicz operator ideals
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.
approximation, Gelfand and Kolmogorov numbers
scientific article; zbMATH DE number 4061992
scientific article