Taylor and Xia spectra of \(p\)-hyponormal \(n\)-tuples
An operator \(T\) on a Hilbert space \({\mathcal H}\) is said to be \(p\)-hyponormal for \(0< p\leq 1\) if \((T^*T)^p\geq (TT^*)^p\). In the case where \(p= 1\) we say simply that \(T\) is hyponormal. By using the Berberian extension theorem for an operator, the author proves the following: If \((A_1,\dots, A_n)\) is an \(n\)-tuple of doubly commuting \(p\)-hyponormal operators, then there is an \(n\)-tuple \((T_1,\dots, T_n)\) of doubly commuting hyponormal operators associated with \((A_1,\dots, A_n)\) such that \((A_1,\dots, A_n)\) and \((T_1,\dots, T_n)\) have the same Taylor spectra and Xia spectra. And, a an application of this, he generalizes the result given by Cho-Curto-Huruya-Zelazko for a Putnam area inequality of above \((T_1,\dots, T_n)\) to the case of \((A_1,\dots, A_n)\).
scientific article; zbMATH DE number 1484694
scientific article