摘要
This paper presents a discussion on a problem suggested by N.Salinas（J.Operator Theory,Vol.10,1983）,i.e.,if T=（T<sub>1</sub>,T<sub>2</sub>,…,T<sub>n</sub>）is a commuting n-tuple ofhyponormal operators on a complex Hilbert space,do we have（1）（2）δ（T-μ）=dist（μ,σ<sub>l</sub>（T））,μ∈C<sup>n</sup>?It is proved that the problems（1）and（2）are both true for some commuting n-tuples ofsemihyponormal operators.In general case,problem（1）has a negative answer.As an ap-plication,we point out that there exists a commuting n-tuple of hyponormal operatorsT（n≥2）,such that|λ|【,where σ<sub>T</sub>（T）denotes J.L.Taylor’sjoint spectra of T,even if the condition of Taylor’s joint spectra of T is given.
This paper presents a discussion on a problem suggested by N.Salinas(J. Operator Theory,Vol.10,1983),i.e.,if T=(T_1,T_2,…,T_n)is a commuting n-tuple of hyponormal operators on a complex Hilbert space,do we have (1) (2)δ(T-μ)=dist(μ,σ_l(T)),μ∈C^n? It is proved that the problems(1)and(2)are both true for some commuting n-tuples of semihyponormal operators.In general case,problem(1)has a negative answer.As an ap- plication,we point out that there exists a commuting n-tuple of hyponormal operators T(n≥2),such that|λ|<,where σ_T(T)denotes J.L.Taylor's joint spectra of T,even if the condition of Taylor's joint spectra of T is given.
