The zero-product problem for Toeplitz operators with radial symbols

Details The zero-product problem for Toeplitz operators with radial symbols The zero-product problem for Toeplitz operators with radial symbols

2007-12-02

arxiv.org/abs/0712.0167v1

Mathematics

Functional Analysis

6 papes

Scientific paper

For any bounded measurable function $f$ on the unit ball $B_n$, let $T_f$ be the Toeplitz operator with symbol $f$ acting on the Bergman space $A^2(B_n)$. The Zero-Product Problem asks: if $f_1,..., f_N$ are bounded measurable functions such that $T_{f_1}... T_{f_N}=0$, does it follow that one of the functions must be zero almost everywhere? This paper give the affirmative answer to this question when all except possibly one of the symbols are radial functions. The answer in the general case remains unknown.

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