Eigenvalue distribution of compact operators
I am going to describe the contents of the book by a collection of quotations from the author's introduction which, in full length, is an excellent source of information on the spirit and the scope of the book, followed by a listing of the key words appearing in the table of contents. ''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 in the last decade. As it turns out, the Lorentz sequence spaces \(\ell_{p,q}\) present a natural framework to formulate precise results on the decay of the eigenvalues. My aim has been to show that methods from the theory of Banach spaces may be used successfully to obtain qualitative estimates on the decay of eigenvalues of abstract classes of maps which, when applied to integral operators, yield extensions of both the classical as well as new results. Applications to eigenvalues of differential operators are not considered in the book.'' Chapter 1: Riesz operators - singular numbers of operators - classical Banach spaces - operator ideals and s-numbers. Chapter 2: Weyl's inequality in Banach spaces - eigenvalues of p-summing operators - interpolation of operator ideals - estimates by single s-numbers. Chapter 3: Kernels with summability conditions - Sobolev spaces - s- numbers of imbedding maps - kernels with differentiability conditions. Chapter 4: Trace formulas - Projection constants.
asymptotic estimates for the eigenvalues of certain types of (power-) compact operators in general Banach spaces
qualitative estimates on the decay of eigenvalues of abstract classes of maps
kernels with differentiability conditions
scientific article; zbMATH DE number 4002857