摘要
We show that a multiplication operator Φ(T)=ATB is normality preserving if and only if it is hyponormality preserving,if and only if it is either of the form A=f(?)g,B=h(?)f, or A=D,B=λD~* for some λ∈C and D E B(H) with D~*D=I.Also we show that Φ is(semi-) Fredholmness prserving if and only if A and B are(semi-)Fredholm operators.
We show that a multiplication operator Φ(T)=ATB is normality preserving if and only if it is hyponormality preserving,if and only if it is either of the form A=f(?)g,B=h(?)f, or A=D,B=λD~* for some λ∈C and D E B(H) with D~*D=I.Also we show that Φ is(semi-) Fredholmness prserving if and only if A and B are(semi-)Fredholm operators.
基金
the Science Foundation of Zhejiang Province and NSF.
