k-hyponormality of powers of weighted shifts via Schur products
英文摘要:
We characterize $k$-hyponormality and quadratic hyponormality of powers of weighted shifts using Schur product techniques.
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Raul E. Curto, Sang Soo Park
We characterize $k$-hyponormality and quadratic hyponormality of powers of weighted shifts using Schur product techniques.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1)-hyponormality for each k>=1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals.
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The algebra of Schur operators on l^2 is known not to be inverse-closed. When l^2=l^2(X) where X is a metric space, we can consider elements of the Schur algebra with certain decay at infinity. For instance if X has the doubling property, then Q. Sun has proved that the weighted Schur algebra for a strictly polynomial weight is inverse-closed. Here, we prove a result dealing with left-invertibility. Namely, if such an operator is bounded below in l^p for some p, then it is bounded below for all q, and it admits a left-inverse in the weighted Schur algebra.
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