Factorization ofk-quasihyponormal operators

[摘要] LetAbe the class of all operatorsTon a Hilbert spaceHsuch thatR(T*kT), the range space ofT*KT, is contained inR(T*k+1), for a positive integerk.It has been shown that ifT ϵ A, there exists a unique operatorCTonHsuch that(i)         T*kT=T*k+1CT ;(ii)        ‖CT‖2=inf{μ:μ≥0  and  (T*kT)(T*kT)*≤μT*k+1T*k+1} ;(iii)       N(CT)=N(T*kT) and(iv)       R(CT)⫅R(T*k+1)¯The main objective of this paper is to characterizek-quasihyponormal; normal, andself-adjoint operatorsTinAin terms ofCT. Throughout the paper, unless statedotherwise,Hwill denote a complex Hilbert space andTan operator onH, i.e., abounded linear transformation fromHintoHitself. For an operatorT, we writeR(T)andN(T)to denote the range space and the null space ofT.

[学科分类] 数学（综合）