A Refined Luecking’s Theorem and Finite-rank Products of Toeplitz Operators
نویسنده
چکیده
Abstract. For any function f in L∞(D), let Tf denote the corresponding Toeplitz operator the Bergman space A(D). A recent result of D. Luecking shows that if Tf has finite rank then f must be the zero function. Using a refined version of this result, we show that if all except possibly one of the functions f1, . . . , fm are radial and Tf1 · · · Tfm has finite rank, then one of these functions must be zero.
منابع مشابه
Algebraic Properties of Toeplitz Operators on the Polydisk
and Applied Analysis 3 For commuting problem, in 1963, Brown and Halmos 2 showed that two bounded Toeplitz operators Tφ and Tψ on the classical Hardy space commute if and only if i both φ and ψ are analytic, ii both φ and ψ are analytic, or iii one is a linear function of the other. On the Bergman space of the unit disk, some similar results were obtained for Toeplitz operators with bounded har...
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تاریخ انتشار 2008