Introduction

Abstract

The purpose of this book is to present asymptotic estimates for the eigenvalues of certain types of (power-)compact operators in general Banach spaces which were proved during the last decade. For linear integral operators, it is a classical problem to relate the order of decay of the eigenvalues to integrability or regularity properties of the defining kernel. While Fredholm, Schur and Carleman treated continuous and, more general, Hilbert-Schmidt kernels, Hille-Tamarkin [31] considered kernels having derivatives belonging to suitable L_p -spaces, i.e. satisfying mixed differentiability and summability conditions. Further results in this direction were achieved and presented by Gohberg-Krein [23]. Lately much more precise estimates were obtained by Birman-Solomjak who in their survey [7] also treat the case of weighted kernel operators on unbounded domains.