Centre-valued Index for Toeplitz Operators with Noncommuting Symbols

Toeplitz operators with matrix-valued symbols and some (unexpected) applications

We discuss the eigenvalue distribution in the Weyl sense of general matrix-sequences associated to a symbol. As a specific case we consider Toeplitz sequences generated by matrix-valued (non Hermitian) bounded functions. We show that the canonical distribution can be proved under mild assumptions on the spectral range of the given symbol. Finally some applications are introduced and discussed.

Subnormal and quasinormal Toeplitz operators with matrix-valued rational symbols

In this paper we deal with the subnormality and the quasinormality of Toeplitz operators with matrix-valued rational symbols. In particular, in view of Halmos’s Problem 5, we focus on the question: Which subnormal Toeplitz operators are normal or analytic ? We first prove: Let Φ ∈ L∞Mn be a matrix-valued rational function having a “matrix pole,” i.e., there exists α ∈ D for which kerHΦ ⊆ (z−α)H...

Toeplitz operators with special symbols

Toeplitz Operators with Essentially Radial Symbols

For Topelitz operators with radial symbols on the disk, there are important results that characterize boundedness, compactness, and its relation to the Berezin transform. The notion of essentially radial symbol is a natural extension, in the context of multiply-connected domains, of the notion of radial symbol on the disk. In this paper we analyze the relationship between the boundary behavior ...

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.