Abstract

In this paper we give a new proof to Theorem 1 in Gu and Zheng (1997). We then provide that $T_f T_g =0$ if and only if $f(z,w)$ or $g(z,w)$ is identically zero where $T_f$ and $T_g$ are two level Toeplitz operators with generating functions $f(z,w)$ and $g(z,w)$ being two variables bounded measurable functions on the unit circle . We also  conjectured zero product of three two level Toeplitz operators.

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