n维单位球面上的Toeplitz符号演算

Toeplitz Symbol Calculus on the Unit Sphere in M^n

探讨了n中单位球面S上Berezin变换和Toep litz算子的性质,证明了由{Tφ,φ∈L∞(S)}所生成的C*-代数I(L∞(S))中算子T的符号恰好为单位球B上函数T(称为T的Berezin变换)的非切向边界值.

In this paper, we investigate the properties of Berezin transform and Toeplitz operators on the unit sphere S in C^n. We obtain the symbol of an operator T in the C^n- algebra （ L^∞ （S）） generated by {Tφ,φ∈L^n（S）｜as the nontangential boundary value of a certain function T （ called the Berezin transform of T ） on the unit ball B.