Let H be a complex Hilbert space, B（H） the set of bounded linear operators on H, C the complex field. For any A, A-1∈B（H）, the operator C=A*-1A is called polar-product operator of A in (1)The properties of C were...Let H be a complex Hilbert space, B（H） the set of bounded linear operators on H, C the complex field. For any A, A-1∈B（H）, the operator C=A*-1A is called polar-product operator of A in (1)The properties of C were studied in (1)In [2], we have used the polar-product to show the solvability of the operator equation λA2+μA*2=αA*A+βAA*（λ, μ, α, β∈C）, and given all its solutions. On discus-展开更多
文摘Let H be a complex Hilbert space, B（H） the set of bounded linear operators on H, C the complex field. For any A, A-1∈B（H）, the operator C=A*-1A is called polar-product operator of A in (1)The properties of C were studied in (1)In [2], we have used the polar-product to show the solvability of the operator equation λA2+μA*2=αA*A+βAA*（λ, μ, α, β∈C）, and given all its solutions. On discus-
