论文标题
toeplitz代数的预测
Projections in Toeplitz algebra
论文作者
论文摘要
由barr {\'i} a-halmos的\ cite [问题19] {barria1982asymptotic}和halmos's \ cite [问题237] {halmos1978a}的动机，我们探索在艰难空间的Toeplitz algebra中的预测。我们表明，当且仅当它是对移位（向后移动）操作员不变的子空间之一的投影时，两个Toeplitz（Hankel）操作员的乘积是投影。结果，人们为Toeplitz操作员和Hankel操作员提供了新的标准证明，使其成为部分异构体。此外，我们完全表征何时toeplitz操作员的自我交流者是一个投影。这提供了Toeplitz代数中的一类非平凡预测。
Motivated by Barr{\'ı}a-Halmos's \cite[Question 19]{barria1982asymptotic} and Halmos's \cite[Problem 237]{Halmos1978A}, we explore projections in Toeplitz algebra on the Hardy space. We show that the product of two Toeplitz (Hankel) operators is a projection if and only if it is the projection onto one of the invariant subspaces of the shift (backward shift) operator. As a consequence one obtains new proofs of criterion for Toeplitz operators and Hankel operators to be partial isometries. Furthermore, we completely characterize when the self-commutator of a Toeplitz operator is a projection. This provides a class of nontrivial projections in Toeplitz algebra.
