One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.Read more
- Gives the most recent results in the area of invariant subspaces
- Relatively self-contained and accessible to beginning researchers
- Summarises standard background results in analysis
Reviews & endorsements
'I think this is a very useful book which will serve as a good source for a rich variety of methods that have been developed for proving positive results on the ISP. Moreover, there is much material in the book which is of interest beyond its application to the ISP. [It] should be of interest to analysts in general as well as being an essential source for study of the ISP.' Sandy Davie, SIAM Review
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: August 2011
- format: Hardback
- isbn: 9781107010512
- length: 298 pages
- dimensions: 229 x 152 x 21 mm
- weight: 0.61kg
- contains: 4 b/w illus. 65 exercises
- availability: Available
Table of Contents
2. The operator-valued Poisson kernel and its applications
3. Properties (An,m) and factorization of integrable functions
4. Polynomially bounded operators with rich spectrum
5. Beurling algebras
6. Applications of a fixed-point theorem
7. Minimal vectors
8. Universal operators
9. Moment sequences and binomial sums
10. Positive and strictly-singular operators
Find resources associated with this titleYour search for '' returned .
Type Name Unlocked * Format Size
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact email@example.com.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×