Trace ideals and their applications
著者
書誌事項
Trace ideals and their applications
（Mathematical surveys and monographs, v. 120）
American Mathematical Society, c2005
2nd ed
- : [pbk.]
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注記
Previous ed.: New York : Cambridge University Press, 1979
Includes bibliographical references (p. 135-147) and index
内容説明・目次
内容説明
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.
目次
- Preliminaries Calkin's theory of operator ideals and symmetrically normed ideals
- convergence theorems for $\mathcal J_P$ Trace, determinant, and Lidskii's theorem $f(x)g(-i\nabla)$ 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.
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