University of Birmingham > Talks@bham > Analysis Seminar > Fredholm theory of Toeplitz operators on Fock spaces

Fredholm theory of Toeplitz operators on Fock spaces

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If you have a question about this talk, please contact Dr. Maria Carmen Reguera.

Toeplitz matrices can easily be defined as infinite matrices constant along the parallels to the main diagonal. Each Toeplitz matrix is generated by a function whose Fourier coefficients are the entries of the matrix. Such matrices generate bounded Toeplitz operators on Hardy spaces of the unit circle when the generating functions are bounded. Despite their simple definition Toeplitz operators have a very rich spectral theory and they form one of the most important classes of nonself-adjoint operators. While the Fredholm properties of Toeplitz operators are well understood in Hardy spaces, much less is known about them in Bergman spaces of the unit disk and even less in Fock spaces of the complex plane.

In this talk I discuss the Fredholm properties of Toeplitz operators acting on standard weighted Fock spaces; in particular, a description of the essential spectrum of a Toeplitz operator generated by a bounded function of vanishing oscillation will be given together with an index formula. Boundedness and compactness of Toeplitz and Hankel operators on these spaces will also be discussed, and the results are compared with those for the other two function spaces.

This talk is part of the Analysis Seminar series.

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