Entropy and Lorentz-Marcinkiewicz Operator Ideals

Abstract

The paper deals with ideals of operators for which the sequence of their entropy numbers(en(T)) belongs to a Lorentz-Marcinkiewicz space `,q, where is a so-called function parameter. In the case (t) = tp the classical Lorentz space `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.