22--hyperreflexivity and hyporeflexivity of power partial isometries

Power partial isometries are not always hyperreflexive neither reflexive. In the present paper it will be shown that power partial isometries are always hyporeflexive and $2$--hyperreflexive

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

Conjugations of Unitary operators, I

If $U$ is a unitary operator on a separable complex Hilbert space $\mathcal{H}$, an application of the spectral theorem says there is a conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on $\mathcal{H}$) for which $C U C = U^{*}.$ In this paper, we fix a unitary operator $U$ and describe all of the conjugations $C$ which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for $U$ if and only if it is invariant for any conjugation $C$ for which $CUC = U^{*}$

Conjugations of Unitary Operators, II

For a given unitary operator $U$ on a separable complex Hilbert space \h, we describe the set $\mathscr{C}_{c}(U)$ of all conjugations $C$ (antilinear, isometric, and involutive maps) on \h for which $C U C = U$. As this set might be empty, we also show that $\mathscr{C}_{c}(U) \not = \varnothing$ if and only if $U$ is unitarily equivalent to $U^{*}$

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