N-hypercontractivity and similarity of Cowen-Douglas operators
| Autor: | Jing Xu, Hyun-Kyoung Kwon, Kui Ji |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Functional Analysis
Numerical Analysis Pure mathematics Algebra and Number Theory 010102 general mathematics 010103 numerical & computational mathematics Shift operator 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis Operator (computer programming) Similarity (network science) FOS: Mathematics Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Eigenvalues and eigenvectors Weighted space Mathematics |
| Zdroj: | Linear Algebra and its Applications. 592:20-47 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2020.01.017 |
| Popis: | When the backward shift operator on a weighted space $H^2_w=\{f=\sum_{j=0} ^{\infty} a_jz^j : \sum_{j=0}^{\infty} |a_j|^2w_j < \infty\}$ is an $n$-hypercontraction, we prove that the weights must satisfy the inequality $$\frac{w_{j+1}}{w_j} \leq {\frac{1+j}{n+j}}.$$ As an application of this result, it is shown that such an operator cannot be subnormal. We also give an example to illustrate the important role that the $n$-hypercontractivity assumption plays in determining the similarity of Cowen-Douglas operators in terms of the curvatures of their eigenvector bundles. 21 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect