Pluriharmonic symbols of commuting Toeplitz operators

Commuting Toeplitz Operators with Pluriharmonic Symbols

By making use of M-harmonic function theory, we characterize commuting Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball or on the Hardy space of the unit sphere in n-dimensional complex space.

Essentially Commuting Toeplitz Operators

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

Toeplitz operators with special symbols

Toeplitz Operators and Toeplitz Algebra with Symbols of Vanishing Oscillation

We study the C∗-algebra generated by Teoplitz operators with symbols of vanishing (mean) oscillation on the Bergman space of the unit ball. We show that the index calculation for Fredholm operators in this C∗-algebra can be easily and completely reduced to the classic case of Toeplitz operators with symbols that are continuous on the closed unit ball. Moreover, in addition to a number of other ...

Hyponormality of Toeplitz Operators with Rational Symbols

In this article we introduce a notion of ‘division’ for rational functions and then give a criterion for hyponormality of Tg+f (f, g are rational functions) in the cases where g divides f . Furthermore we show that we may assume, without loss of generality, that g divides f when we consider the hyponormality of Tg+f .