ON REFLEXIVITY OF CC-SYMMETRIC OR SKEW-CC-SYMMETRIC OPERATORS (Recent developments of operator theory by Banach space technique and related topics)

We present results concerning reflexivity and hyperreflexivity of a subspace of all C-symmetric operators from [6] and a subspace of all skew-C-symmetric operators from [2] with a given conjugation C. We also give a description of theirs preanihilators

ASYMMETRIC TRUNCATED TOEPLITZ OPERATORS AND ITS CHARACTERIZATIONS BY RANK TWO OPERATORS (Recent developments of operator theory by Banach space technique and related topics)

When investigating truncated Toeplitz operators, the question of considering two different model spaces naturally appears. The goal of this paper is to present asymmetric truncated Toeplitz operators with L^{2} symbols between two different model spaces given by inner functions such that one divides the other. Asymmetric truncated Toeplitz operators can be characterized in terms of operators of rank at most two. Mainly, the results from [6] are presented