Weakly k-hyponormal and polynomially hyponormal commuting operator pairs
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- 作者：YongJiang Duan ; TingTing Qi
- 关键词：weakly k ; hyponormal ; k ; hyponormal ; polynomially hyponormal ; subnormal ; commuting operator pair ; 47B20 ; 47B37 ; 47B38 ; 47A13
- 刊名：SCIENCE CHINA Mathematics
- 出版年：2015
- 出版时间：February 2015
- 年：2015
- 卷：58
- 期：2
- 页码：405-422
- 全文大小：315 KB
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文摘
We introduce the notion of weak k-hyponormality and polynomial hyponormality for commuting operator pairs on a Hilbert space and investigate their relationship with k-hyponormality and subnormality. We provide examples of 2-variable weighted shifts which are weakly 1-hyponormal but not hyponormal. By relating the weak k-hyponormality and k-hyponormality of a commuting operator pair to positivity of restriction of some linear functionals to corresponding cones of functions, we prove that there is an operator pair that is polynomially hyponormal but not 2-hyponormal, generalizing Curto and Putinar’s result (1991, 1993) to the two-variable case.