Sibel Şahin
Assistant Professor at the Department of Mathematics at the Mimar Sinan Fine Arts University.
Title: Approximation Numbers: From Kolmogorov Numbers to Differences of Composition Operators
Abstract:
Joint work with Frédéric Bayart of Laboratoire de Mathématiques Blaise Pascal.
In this talk we will first consider various singular numbers of operators which happen to be equivalent in the Hilbert space setting. Through Kolmogorov numbers we will first see how these singular entities for composition operators relate to complex potential theory, namely Monge-Amp`ere capacity. In the second part we will relate the component structure of bounded composition operators to the function theoretic properties of the symbols and for this we will focus on the approximation numbers of differences of composition operators. We will see how one can obtain optimal upper and lower bounds for approximation numbers of differences using classical singular invariants like Bernstein and Gelfand numbers and specific choices of Blaschke products from the underlying function space.
References:
1. G. Lechner, D. Li, H. Queffélec, L. Rodriguez-Piazza: Approximation numbers of weighted composition operators. Journal of Functional Analysis 274, 1928–1958 (2018).
2. J. Moorhouse, C. Toews: Differences of composition operators. Contemporary Mathematics 321, 207–213 (2003).
3. H. Queffélec, K. Seip: Decay rates for approximation numbers of composition operators. Journal d’Analyse Mathématique 125, 371–399 (2015).