zbMATH — the first resource for mathematics

The spectrum of a composition operator and Calderón’s complex interpolation. (English) Zbl 1217.47050
Ball, Joseph A. (ed.) et al., Topics in operator theory. Volume 1: Operators, matrices and analytic functions. Proceedings of the 19th international workshop on operator theory and applications (IWOTA), College of William and Mary, Williamsburg, VA, USA, July 22–26, 2008. A tribute to Israel Gohberg on the occasion of his 80th birthday. Basel: Birkhäuser (ISBN 978-3-0346-0157-3/hbk; 978-3-0346-0163-4/set; 978-3-0346-0158-0/ebook). Operator Theory: Advances and Applications 202, 451-467 (2010).
The paper gives a uniform approach to the spectrum of composition operators induced by automorphisms of the unit disk acting on weighted Dirichlet spaces, which includes the Hardy space, the Bergman space, and the classical Dirichlet space.
For the entire collection see [Zbl 1181.47002].
Reviewer: Kehe Zhu (Albany)

47B33 Linear composition operators
46B70 Interpolation between normed linear spaces
47A10 Spectrum, resolvent