Eigenvalue distribution of compact operators
type: Item
instance of: scholarly article
title: Eigenvalue distribution of compact operators
zbMATH Open document ID: 0618.47013
published in: Operator Theory: Advances and Applications
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47-02
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 4002857
zbMATH Keywords: Weyl numbers
zbMATH Keywords: asymptotic estimates for the eigenvalues of certain types of (power-) compact operators in general Banach spaces
zbMATH Keywords: Lorentz sequence spaces
zbMATH Keywords: qualitative estimates on the decay of eigenvalues of abstract classes of maps
zbMATH Keywords: integral operators
zbMATH Keywords: Riesz operators
zbMATH Keywords: singular numbers
zbMATH Keywords: Weyl's inequality
zbMATH Keywords: p-summing operators
zbMATH Keywords: interpolation of operator ideals
zbMATH Keywords: Kernels with summability conditions
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: s-numbers of imbedding maps
zbMATH Keywords: kernels with differentiability conditions
zbMATH Keywords: Trace formulas
zbMATH Keywords: Projection constants
author: Hermann König
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4002857