Weakly k-hyponormal and polynomially hyponormal commuting operator pairs

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...

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Bibliographic Details
Published in:Science China. Mathematics 2015-02, Vol.58 (2), p.405-422
Main Authors: Duan, YongJiang, Qi, TingTing
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
加权
多项式
希尔伯特空间
线性泛函
运营商
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-014-4916-x