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Complex symmetric composition operators on weighted Hardy spaces.
- Source :
- Proceedings of the American Mathematical Society; May2020, Vol. 148 Issue 5, p2117-2127, 11p
- Publication Year :
- 2020
-
Abstract
- Let φ be an analytic self-map of the open unit disk D. We study the complex symmetry of composition operators C<subscript>φ</subscript> on weighted Hardy spaces induced by a bounded sequence. For any analytic self-map of D that is not an elliptic automorphism, we establish that if C<subscript>φ</subscript> is complex symmetric, then either φ (0) = 0 or φ is linear. In the case of weighted Bergman spaces A<superscript>2</superscript><subscript>α</subscript>, we find the non-automorphic linear fractional symbols φ such that C<subscript>φ</subscript> is complex symmetric. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 148
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 142355089
- Full Text :
- https://doi.org/10.1090/proc/14909