In this note we consider the hyponormality of Toeplitz operators Tφ on the Weighted Bergman space Aα(D) with symbol in the class of functions f + g with polynomials f and g of degree 2. Mathematics subject classification (2010): 47B20, 47B35.

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

A survey of the theory of k-hyponormal operators starts with the construction of a polynomially hyponormal operator which is not subnormal. This is achieved via a natural dictionary between positive functionals on specific convex cones of polynomials and linear bounded operators acting on a Hilbert space, with a distinguished cyclic vector. The class of unilateral weighted shifts provides an op...

We study the boundedness and compactness of generalized Volterra integral operator on weighted Bergman spaces with doubling weights unit disc. A Toeplitz is defined boundedness, Schatten class membership this are investigated Hilbert space. As an application, operators also characterized. Finally, we get characterizations Hardy space $$H^2$$ .

Toeplitz operators (or equivalently, Wiener-Hopf operators; more generally, block Toeplitz operators; and particularly, Toeplitz determinants) are of importance in connection with a variety of problems in physics, and in particular, in the field of quantum mechanics. For example, a study of solvable models in quantum mechanics uses the spectral theory of Toeplitz operators (cf. [Pr]); the one-d...

Abstract In this paper, we obtain some interesting reproducing kernel estimates and Carleson properties that play an important role. We characterize the bounded compact Toeplitz operators on weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, estimate essential norm them assuming they are bounded.

Unlike Toeplitz operators on H, 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 eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several e...