On a class of jointly hyponormal Toeplitz operators

We characterize when a pair of Toeplitz operators T = (T Φ , T ψ ) is jointly hyponormal under various assumptions--for example, Φ is analytic or Φ is a trigonometric polynomial or Φ - ψ is analytic. A typical characterization states that T = (T Φ , T ψ ) is jointly hyponormal if and only if an algebraic relation of Φ and ψ holds and the single Toeplitz operator T ω is hyponormal, where ω is a combination of Φ and ψ. More general results for an n-tuple of Toeplitz operators are also obtained.

我们在各种假设下刻画了一对托普利兹算子\(T=(T_{\Phi},T_{\psi})\)何时是联合亚正规的——例如，\(\Phi\)是解析的，或者\(\Phi\)是三角多项式，或者\(\Phi - \psi\)是解析的。一个典型的刻画表明，\(T=(T_{\Phi},T_{\psi})\)是联合亚正规的当且仅当\(\Phi\)和\(\psi\)满足一个代数关系并且单个托普利兹算子\(T_{\omega}\)是亚正规的，其中\(\omega\)是\(\Phi\)和\(\psi\)的一种组合。对于\(n\)元托普利兹算子也得到了更一般的结果。