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|Title:||Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions||Authors:||Abanin, Alexander V.
Khoi, Le Hai
Tien, Pham Trong
|Keywords:||Science::Mathematics||Issue Date:||2019||Source:||Abanin, A. V., Khoi, L. H. & Tien, P. T. (2019). Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions. Bulletin Des Sciences Mathematiques, 158, 102806-. https://dx.doi.org/10.1016/j.bulsci.2019.102806||Project:||M4011724.110 (RG128/16)||Journal:||Bulletin des Sciences Mathematiques||Abstract:||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.||URI:||https://hdl.handle.net/10356/150814||ISSN:||0007-4497||DOI:||10.1016/j.bulsci.2019.102806||Rights:||© 2019 Elsevier Masson SAS. All rights reserved. This paper was published in Bulletin des Sciences Mathematiques and is made available with permission of Elsevier Masson SAS.||Fulltext Permission:||embargo_20220307||Fulltext Availability:||With Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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