The finite rank theorem for Toeplitz operators in the Fock space

TL;DR

This paper proves that finite-rank Toeplitz operators with function symbols in the Fock space must be zero, removing previous restrictions like compact support through a novel proof method.

Contribution

It introduces a new proof technique for finite-rank theorems that eliminates the need for symbols to have compact support.

Findings

Finite-rank Toeplitz operators with function symbols are zero.

The new method avoids previous support restrictions.

The theorem applies under more general conditions.

Abstract

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.