MMN-5330
The (non-)extendability of Embry’s Theorem
Hranislav Stanković;Abstract
Let \( A, P, T \in \mathfrak{B}(\mathcal{H}) \) be such that \( P \) is an orthogonal projection commuting with \( A \) and \( 0 \notin \mathcal{W}(T) \). We prove that if \( PT = TA \), then \( A = P \). As a consequence, Embry's Theorem on the similarity of normal operators follows easily from our result. Furthermore, we demonstrate that this theorem cannot be extended to quasinormal operators, thereby providing a negative answer to a conjecture posed by Mortad in \cite{Mortad10}.
Vol. 27 (2026), No. 1, pp. 373-378