In this article, we concentrate on the Berezin transform of the absolute value of a bounded linear operator defined on the Bergman space of the open unit disk. We establish some sufficient conditions on which guarantee that the Berezin transform of majorizes the Berezin transform of . We have shown that is self-adjoint and if and only if there exists a normal idempotent operator on such that , where is the Berezin transform of . We also establish that if is compact and for some , , then for all . Further, if is the polar decomposition of , then we present necessary and sufficient conditions on such that intertwines with and a contraction belonging to .
"Berezin transform of the absolute value of an operator." Ann. Funct. Anal. 9 (2) 151 - 165, May 2018. https://doi.org/10.1215/20088752-2017-0035