Related papers: Normal Truncated Toeplitz Operators
We show that truncated Toeplitz operators are characterized by a collection of complex symmetries. This was conjectured by Klis-Garlicka, Lanucha, and Ptak, and proved by them in some special cases.
It was recently proved that in some special cases asymmetric truncated Toeplitz operators can be characterized in terms of compressed shifts and rank-two operators of special form. In this paper we show that such characterizations hold in…
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and…
Truncated Toeplitz operators are C--symmetric with respect to the canonical conjugation given on an appropriate model space. However, by considering only one conjugation one cannot characterize truncated Toeplitz operators. It will be…
In the last decade, a large amount of research has been concentrated on the operators living on the model space. Asymmetric truncated Toeplitz operators and asymmetric truncated Hankel operators are the natural generalization of truncated…
We give a complete description of the finite-rank truncated Toeplitz operators.
We find necessary and sufficient conditions for the product of two truncated Toeplitz operators on a model space to itself be a truncated Toeplitz operator, and as a result find a characterization for the maximal algebras of bounded…
The aim of this paper is to investigate asymmetric truncated Toeplitz operators with $L^2$ symbols between two different model spaces given by inner functions such that one divides the other. Characterizations of these operators are given…
We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the $H^2$ and $H^{\infty}$ norms of functions in model spaces.
Truncated Toeplitz operators in a model space are C--symmetric with respect to a natural conjugation in that space. We show that this and another conjugation associated to an orthogonal decomposition possess unique properties and we study…
Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of…
Matrix valued truncated Toeplitz operators act on vector-valued model spaces. They represent a generalization of block Toeplitz matrices. A characterization of these operators analogue to the scalar case is obtained, as well as the…
In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated…
In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric…
This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason's seminal paper in 2007.
In this paper we investigate operators unitarily equivalent to truncated Toeplitz operators. We show that this class contains certain sums of tensor products of truncated Toeplitz operators. In particular, it contains arbitrary inflations…
Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators.…
We obtain an analogue of Coburn's description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated…
Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct…
We characterize matrix-valued asymmetric truncated Toeplitz operators (which are compressions of multiplication operators acting between two possibly different model spaces) by using compressed shifts, modified compressed shifts and shift…