Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorKato, Tosio. author
TitleA Short Introduction to Perturbation Theory for Linear Operators [electronic resource] / by Tosio Kato
ImprintNew York, NY : Springer US, 1982
Connect to
Descript XIV, 162 p. online resource


This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehenยญ sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have nonยญ trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatterยญ ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools


One Operator theory in finite-dimensional vector spaces -- ยง 1. Vector spaces and normed vector spaces -- ยง 2. Linear forms and the adjoint space -- ยง 3. Linear operators -- ยง 4. Analysis with operators -- ยง 5. The eigenvalue problem -- ยง 6. Operators in unitary spaces -- ยง 7. Positive matrices -- Two Perturbation theory in a finite-dimensional space -- ยง 1. Analytic perturbation of eigenvalues -- ยง 2. Perturbation series -- ยง 3. Convergence radii and error estimates -- ยง 4. Similarity transformations of the eigenspaces and eigenvectors -- ยง 5. Non-analytic perturbations -- ยง 6. Perturbation of symmetric operators -- ยง 7. Perturbation of (essentially) nonnegative matrices -- Notation index -- Author index

Mathematics Mathematical analysis Analysis (Mathematics) Physics Mathematics Analysis Theoretical Mathematical and Computational Physics


Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network


facebook   instragram