The Rademacher complexity of linear transformation classes. (English) Zbl 1147.68542
Lugosi, Gabor (ed.) et al., Learning theory. 19th annual conference on learning theory, COLT 2006, Pittsburgh, PA, USA, June 22–25, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-35294-5/pbk). Lecture Notes in Computer Science 4005. Lecture Notes in Artificial Intelligence, 65-78 (2006).
Summary: We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space \(\mathcal H^2\). This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov–Clark measures.
For the entire collection see [Zbl 1107.68015].
For the entire collection see [Zbl 1107.68015].
MSC:
| 68Q32 | Computational learning theory |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 47B07 | Linear operators defined by compactness properties |
| 47N30 | Applications of operator theory in probability theory and statistics |
