Finite-Rank Products of Toeplitz Operators in Several Complex Variables期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Finite-Rank Products of Toeplitz Operators in Several Complex Variables

Authors:	Trieu Le

Affiliation:	(1) Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Abstract:	For any α > −1, let A²_α be the weighted Bergman space on the unit ball corresponding to the weight (1 – \|z\|²)^α. We show that if all except possibly one of the Toeplitz operators $T_{f_{1} },ldots,T_{f_{r}}$ are diagonal with respect to the standard orthonormal basis of A²_α and $T_{f_{1}} cdots T_{f_{r}}$ has finite rank, then one of the functions $f_{1} ,ldots, f_{r}$ must be the zero function.

Keywords:	KeywordHeading" >. Toeplitz operator weighted Bergman space finite-rank product
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