范数恒等式与最大算子数值域

The Norm Equality and Maximal Numerical Range

首先给出了Banach空间上范数恒等式成立的等价条件,其次研究了Hilbert空间上范数恒等式成立的充分必要条件.进一步讨论了范数恒等式与线性泛函和算子数值域、最大算子数值域及数值域半径之间的关系.所得结果推广了M.Barraa等人(2001年)的部分结果.

The equivalent condition of the norm equality in Banach space is discussed in this paper, some sufficient and necessary conditions are obtained for norm equality in Hilbert space. Then, the spectrum radius of numerical range and linear functional are considered. In addition, the results obtained by M. Barraa and M. Boumazgour （2001） are generalized.