Trace Ideals and Their Applications: Second Edition (Mathematical Surveys and Monographs)

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. This Is A Second Edition Of A Well-known Book 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 Second 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.--book Jacket. Ch. 1. Preliminaries -- Ch. 2. Calkin's Theory Of Operator Ideals And Symmetrically Normed Ideals; Convergence Theorems For J[subscript P] -- Ch. 3. Trace, Determinant, And Lidskii's Theorem -- Ch. 4. F(x)g(-i[actual Symbol Not Reproducible]) -- Ch. 5. Fredholm Theory -- Ch. 6. Scattering With A Trace Condition -- Ch. 7. Bound State Problems -- Ch. 8. Lots Of Inequalities -- Ch. 9. Regularized Determinants And Renormalization In Quantum Field Theory -- Ch. 10. Introduction To The Theory On A Banach Space -- Ch. 11. Borel Transforms, The Krein Spectral Shift, And All That -- Ch. 12. Spectral Theory Of Rank One Perturbations -- Ch. 13. Localization In The Anderson Model Following Aizenman-molchanov -- Ch. 14. Xi Function. Barry Simon. Includes Bibliographical References (p. 135-147) And Index.

From a review of the first edition: Beautifully written and well organized ... indispensable for those interested in certain areas of mathematical physics ... for the expert and beginner alike. The author deserves to be congratulated both for his work in unifying a subject and for showing workers in the field new directions for future development. —Zentralblatt MATH This is a second edition of a well-known book 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 second 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.

These expository lectures contain an advanced technical account of a branch of mathematical analysis. In his own lucid and readable style the author begins with a comprehensive review of the methods of bounded operators in a Hilbert space. He then goes on to discuss a wide variety of applications including Fredholm theory and more specifically his own specialty of mathematical quantum theory. included also are an extensive and up-to-date list of references enabling the reader to delve more deeply into this topical subject.