等距同构的Toeplitz算子

The Isometric Isomorphism of Toeplitz Operators on Lpa(Bn)

在讨论Ｌｐａ（Ｂｎ）上的等距及等距同构的Ｔｏｅｐｌｉｔｚ算子的基础上，对于１＜ｐ＜∞，ｐ≠２，证明了Ｌｐａ（Ｂｎ）上两个Ｔｏｅｐｌｉｔｚ算子Ｔｆ与Ｔｇ等距同构的充分必要条件是：存在ψ∈Ａｕｔ（Ｂ），使得ｇ（ｚ）＝ｆ（ψ（ｚ））．

Considering for 1<p<∞,p≠2,it is shown that a pair of Toeplitz operators Tf and Tg on Lpa(Bn) is isometrically isomorphic if and only if there is a ψ∈Aut(B),so that g(z)=f(ψ(z)).