In a recent paper [11], R.E. Curto, S.H. Lee and J. Yoon asked the following question. Let A be a subnormal operator, and assume that $A^2$ is quasinormal. Does it follow that A is quasinormal? In this paper, we answer that question in the affirmative. In fact, we prove a more general result that subnormal nth roots of quasinormal operators are quasinormal. Research on this problem has led us to a new criterion for a semispectral measure on the half-line to be spectral, written in terms of its two “moments”.

中文翻译：

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次正规ñ拟正规运营的日根拟正规

RE Curto，SH SH Lee和J. Yoon在最近的一篇论文[11]中提出了以下问题。令A为次正规算子，并假设 ${\mathrm{一个}}^{\mathrm{2个}}$ 是准正常的。遵循A是准正规的吗？在本文中，我们肯定地回答了这个问题。实际上，我们证明了一个更一般的结果，即准正规算子的第n个次正规根是准正规的。对这个问题的研究使我们找到了一条新标准，以半光谱谱线的两个“矩”来表示半光谱谱。