有界线性算子的n-次数值域

On the n-numerical range of a bounded inear operator

研究Hilbert空间H上的有界线性算子的n-次数值域的性质,n-次数值域与算子谱及n-次数值域之间的关系.将算子的二次数值域推广到n-次数值域,发现n-次数值域具有一系列与二次数值域类似的性质;在一定条件下,n-次数值域包含在二次数值域中.当空间是有限维时,算子的n-次数值域就等于算子的谱.

The nnumerical range is presented.The main results are a spectral inclusion theorem and the relation amogng nnumerical ranges. During the course of developing the quadratic numerical range into nnumerical range,the nnumerical range has the similur properties with the quadratic numerical and is contained in the quadratic numerical under condition.Especially,the nnumerical range equals the spectrum of operator when the dimension of the space is finite.