Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
| Autor: | Pham Trong Tien, Le Hai Khoi, Alexander V. Abanin |
|---|---|
| Přispěvatelé: | School of Physical and Mathematical Sciences |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics [Science]
Connected space Component (thermodynamics) General Mathematics 010102 general mathematics Structure (category theory) Banach space Holomorphic function Composition (combinatorics) Topology Compact operator Space (mathematics) 01 natural sciences Composition Operator Topological Structure 0101 mathematics Mathematics |
| Popis: | We consider the topological structure problem for the space of composition operators as well as the space of weighted composition operators on weighted Banach spaces with sup-norm. For the first space, we prove that the set of all composition operators that differ from the given one by a compact operator is path connected; however, in general, it is not always a component. Furthermore, we show that the set of compact weighted composition operators is path connected, but it is not a component in the second space. Ministry of Education (MOE) Accepted version The authors would like to thank the referees for useful remarks and comments that led to the improvement of the paper. The main part of this article has been done during Pham Trong Tien’s stay at Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the institution for hospitality and support. |
| Databáze: | OpenAIRE |
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