A note on Putinar's matricial models

In this note we consider the conjecture that every hyponormal Putinar's matricial model of rank two is subnormal. Related to this conjecture, we show that there exists a non rationally cyclic subnormal Putinar's matricial model of rank two and then give a sufficient condition for it to be a subnormal operator.

A Subnormal Operator and its Dual

It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.