Buch, Englisch, 150 Seiten
Buch, Englisch, 150 Seiten
Reihe: Mathematical Surveys and Monographs
ISBN: 978-0-8218-3581-4
Verlag: American Mathematical Society
This is a second edition of a well-known book stemming from the author's lectures on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this edition, the author has added four chapters on the closely related theory of rank one perturbations of self-adjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published. This book continues to be a vital source of information for those interested in the theory of trace ideals and in its applications to various areas of mathematical physics.
Contents
- Preliminaries
- Calkin's theory of operator ideals and symmetrically normed ideals; convergence theorems for $mathcal J P$
- Trace, determinant, and Lidskii's theorem
- $f(x)g(-inabla)$
- Fredholm theory
- Scattering with a trace condition
- Bound state problems
- Lots of inequalities
- Regularized determinants and renormalization in quantum field theory
- An introduction to the theory on a Banach space
- Borel transforms, the Krein spectral shift, and all that
- Spectral theory of rank one perturbations
- Localization in the Anderson model following Aizenman-Molchanov
- The Xi function
- Addenda
- Bibliography
- Index
- Preliminaries
- Calkin's theory of operator ideals and symmetrically normed ideals; convergence theorems for $mathcal J P$
- Trace, determinant, and Lidskii's theorem
- $f(x)g(-inabla)$
- Fredholm theory
- Scattering with a trace condition
- Bound state problems
- Lots of inequalities
- Regularized determinants and renormalization in quantum field theory
- An introduction to the theory on a Banach space
- Borel transforms, the Krein spectral shift, and all that
- Spectral theory of rank one perturbations
- Localization in the Anderson model following Aizenman-Molchanov
- The Xi function
- Addenda
- Bibliography
- Index
Zielgruppe
Graduate students and research mathematicians interested in the theory of operators and its applications to mathematical physics.
