Hyponormal Toeplitz Operators on the Dirichlet Spaces

Hyponormal Toeplitz Operators on the Weighted Bergman Spaces

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.

Fredholm Properties of Toeplitz Operators on Dirichlet Spaces

In this paper, the Fredholm properties of some Toeplitz operators on Dirichlet spaces be discussed, and the essential spectra of Toeplitz operators with symbols in C 1 or H ∞ 1 + C 1 be computed.

Toeplitz Operators on Fock Spaces

Superposition Operators on Dirichlet Spaces

In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. T...

On the Hyponormal Property of Operators

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...