The zero-product problem for Toeplitz operators with radial symbols

2007/12/02 by Trieu Le, Le, Trieu
Mathematics · #47B35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47B35

paper · pdf · doi:10.48550/arxiv.0712.0167

6 papes

arxiv created 2007/12/02 · arxiv updated 2009/12/01

Abstract

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 A²(B_n). The Zero-Product Problem asks: if f₁,..., f_N are bounded measurable functions such that T_f1... T_fN=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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