Let A be a Banach algebra which does not contain any nonzero idempotent element, let γ > 0, and letWe also show, assuming a suitable spectral condition on x, that if x ≥ 1 − 1 (γ + 1)

In this paper we study when the product of two dilations of truncated Toeplitz operators gives a dilation of a truncated Toeplitz operator. We will use an approach established in a recent paper written by Ko and Lee. This approach allows us to represent the dilation of the truncated Toeplitz operator via a 2 × 2 block operator.

In the present paper, we study spectral properties of Toeplitz operators with (quasi-) radial symbols on Bergman space. More precisely, the problem we are interested in is to understand when a given Toeplitz operator belongs to a Schatten-von Neumann class. The methods of the approximation theory (i.e., Legendre polynomials) are used to advance in this direction.

In this Erratum we would like to clarify statement and the proof of Theorem 2 in our paper: ”Zero-based invariant subspaces in the Bergman space Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(1) (2018), 277-285.”

A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is to fully characterize the set of all Toeplitz operators that commute with a given one. In [2], the second author described the sum S = T e imθ f +T e ilθ g , where f and g are radial functions, that commutes with the sum T = T e ipθ r (2M +1)p + T e isθ r (2N +1)s . It is proved that S = cT , where c is a constant. In this article, we shall replace r (2M +1)p and r (2N+1)s by r n and r d respectively, with n and d in N, and we shall show that the same result holds.