Abstract. In this paper we show that the normal parts of quasisimilar loghyponormal operators are unitarily equivalent. A Fuglede-Putnam type theorem for log-hyponormal operators is proved. Also, it is shown that a log-hyponormal operator that is quasisimilar to an isometry is unitary and that a log-hyponormal spectral operator is normal.2000 Mathematics Subject Classification. 47B20.
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