摘要： For bounded linear operators A and B on Hilbert spaces H and K , respectively, it is known that the numerical radii of A , B and A ⊗ B are related by the inequalities w ( A ) w ( B ) ≤ w ( A ⊗ B ) ≤ min { ‖ A ‖ w ( B ) , w ( A ) ‖ B ‖ } . In this paper, we show that (1) if w ( A ⊗ B ) = w ( A ) w ( B ) , then w ( A ) = ρ ( A ) or w ( B ) = ρ ( B ), where ρ (·) denotes the spectral radius of an operator, and (2) if A is hyponormal, then w ( A ⊗ B ) = w ( A ) w ( B ) = ‖ A ‖ w ( B ) . Here (2) confirms a conjecture of Shiu’s and is proven via dilating the hyponormal A to a normal operator N with the spectrum of N contained in that of A . The latter is obtained from the Sz.-Nagy–Foiaş dilation theory. 其他題名： Integr. Equ. Oper. Theory 出版者： Basel: Springer Basel 出版日期： 2014-03 出處： Integral equations and operator theory, 2014-03, Vol.78 (3), p.375-382 資源來源： SpringerLink Journals 版權： Springer Basel 2013 識別號： ISSN: 0378-620X 識別號： EISSN: 1420-8989 識別號： DOI: 10.1007/s00020-013-2098-5
