THE CLASS OF COMPLEX SYMMETRIC OPERATORS IS NOT NORM CLOSED.

An operator T ∊ B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C : H →H so that CTC = T. In this paper, a class of complex symmetric operators on finite dimensional Hilbert spaces is constructed. As an application, it is shown that Kakutani's unilateral weighted shift operator is not complex symmetric; however, it is a norm limit of complex symmetric operators. This gives a negative answer to a question of S. Garcia and W. Wogen: that is, whether or not the class of complex symmetric operators is norm closed. [ABSTRACT FROM AUTHOR]