Some Quadratically Hyponormal Weighted Shifts
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In the study of the gaps between subnormality and hyponormality both quadratic hyponormality and the related property positive quadratic hyponormality have been considered, especially for weighted shift operators. In particular, these have been studied for shifts with the first two weights equal and with Bergman tail or recursively generated tail. In this article, we characterize the allowed first two equal weights for quadratic hyponormality with Bergman tail, and the allowed first two equal weights for positive quadratic hyponormality with recursively generated tail.
Mathematics Subject Classification (2000).47B37 47B20
Keywords.Quadratically hyponormal positively quadratically hyponormal recursively generated weighted shift Bergman shift
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