A necessary and sufficient condition for a bounded operator to be a composition operator is investigated in this paper. Normal, quasi-hyponormal, paranormal composition operators are characterised.
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Huang, S. (2008). Weighted composition operators on Lorentz spaces [master's thesis, The University of Hong Kong]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0029-1812201200013912