Some notes on complex symmetric operators
Authors: Marcos S. Ferreira
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2021 · Pages: 90 - 96
Published Online: 03 Dec 2021
Abstract: In this paper we show that every conjugation C on the Hardy-Hilbert space H2 is of type C=T*J T, where T is an unitary operator and J f(z)=f(z) with f∈H2. Moreover, we prove some relations of complex symmetry between the operators T and |T|, where T =U|T| is the polar decomposition of bounded operator T(H) on the separable Hilbert space H.
Keywords: Hardy space, Toeplitz operator, complex symmetric operator, Aluthge transform