On self-dual subnormal operators (Q1804037)

Let \(S\in B(H)\) be a subnormal operator, and let \(N\in B(K)\) be its minimal normal extension. Then \(N\) can be written as a \(2\times 2\) matrix \(N={S\;X\choose O\;T^*}\) with respect to the decomposition \(K=H\oplus H^ \perp\). In the case where \(S\) is pure (i.e., \(S\) has no normal part), \(T\) is called the dual of \(S\) and, particularly, if \(S\) is unitarily equivalent to its dual \(T\), then \(S\) is said to be self-dual. These definition was introduced by J. B. Conway. In this paper, the author generalizes the result of C. C. Huang about self-dual subnormal operators, and considers the converse of this result.