Matrix Representations of Asymmetric Truncated Toeplitz Operators

Abstract

In this paper, we describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces $$K_1$$ K 1 and $$K_2$$ K 2 . The novelty of our approach is that here we consider matrix representations computed with respect to bases of different type in $$K_1$$ K 1 and $$K_2$$ K 2 (for example, kernel basis in $$K_1$$ K 1 and conjugate kernel basis in $$K_2$$ K 2 ). We thus obtain new matrix characterizations which are simpler than the ones already known for asymmetric truncated Toeplitz operators.

Asymmetric Truncated Hankel Operators: Rank One, Matrix Representation

“…and since C β BJ # and J # BC α are ATTOs by Theorem 4 ([10]), then we can deduce the matrix representation of an ATTO with respect to kernel and conjugate kernel bases, and to conjugate kernel and kernel bases in both finite and infinite dimensional cases, which matches with the work done in [14].…”

Characterizations of Matrix Valued Asymmetric Truncated Toeplitz Operators

“…on the unit circle T = ∂D = {z ∈ C : |z| = 1}. Since D. Sarasons paper [26] TTO's, and later on ATTO's [3,6,7], have been intensly studied (see [1,8,10,12,14,27] and [5,[15][16][17][18]22,23]).…”