The closures of (U+K)-orbits of essentially normal triangular operator models  

作　　者：ZHAI FaHui 1,& GUO XianZhou 2 1 Department of Mathematics,Qingdao University of Science and Technology,Qingdao 266061,China 2 School of Sciences,Hebei University of Technology,Tianjin 300401,China 

出　　处：《Science China Mathematics》2010年第4期1045-1066,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10701031,10571041)

摘　　要：The (U + K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as (U + K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the (U + K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρ F (T)} and σ p (T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed (U + K)-orbit if they have the same spectral picture,and describe the closures of the (U + K)-orbits of these operator models.These generalize some known results on the closures of (U + K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article "A survey of (U + K)-orbits".The (U + K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as (U + K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the (U + K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρ F (T)} and σ p (T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed (U + K)-orbit if they have the same spectral picture,and describe the closures of the (U + K)-orbits of these operator models.These generalize some known results on the closures of (U + K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article 'A survey of (U + K)-orbits'.

关 键 词：(U+K)-orbit essentially NORMAL OPERATOR TRIANGULAR OPERATOR 

分 类 号：O177.1[理学—数学]