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Aluthge transforms of unbounded weighted composition operators in L 2 ‐spaces
Author(s) -
Benhida Chafiq,
Budzyński Piotr,
Trepkowski Jacek
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800503
Subject(s) - mathematics , composition (language) , composition operator , closure (psychology) , pure mathematics , transformation (genetics) , function space , operator (biology) , mathematical analysis , hilbert space , multiplication operator , chemistry , repressor , economics , philosophy , linguistics , biochemistry , transcription factor , market economy , gene
We describe the Aluthge transform of an unbounded weighted composition operator acting in an L 2 ‐space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p ‐hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones.