The finite rank theorem for Toeplitz operators in the Fock space

Alexandre Borichev (1) , Grigori Rozenblum (2)

1 I2M - Institut de Mathématiques de Marseille
2 Chalmers University of Technology [Göteborg]

We consider Toeplitz operators in the Fock space, under rather general conditions imposed on the symbols. It is proved that if the operator has finite rank and the symbol is a function then the operator and the symbol should be zero. The method of proving is different from the one used previously for finite rank theorems, and it enables one to get rid of the compact support condition for symbols imposed previously.

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Alexandre Borichev, Grigori Rozenblum. The finite rank theorem for Toeplitz operators in the Fock space. Journal of Geometric Analysis, 2015, 25, pp.347-356. ⟨hal-01114540⟩