Weakly k-hyponormal and polynomially hyponormal commuting operator pairs  

作　　者：DUAN Yong Jiang QI Ting Ting 

机构地区：[1]School of Mathematics and Statistics, Northeast Normal University

出　　处：《Science China Mathematics》2015年第2期405-422,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(GrantNos.10801028 and 11271075);Science and Technology Development Planning Program of Jilin Province(GrantNo.201215008);Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120043120003)

摘　　要：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.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.

关 键 词：weakly k-hyponormal k-hyponormal polynomially hyponormal SUBNORMAL commuting operator pair 

分 类 号：O174.14[理学—数学] O177.1[理学—基础数学]