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In Yoshino, Proc. Amer. Math. Soc. 95: 571–572, 1985 the author proved that for a 𝑀-hyponormal operator 𝐴* and for a dominant operator 𝐵, 𝐶𝐴 = 𝐵𝐶 implies 𝐶𝐴* = 𝐵*𝐶. In the case where 𝐴* and 𝐵 are normal, this result is known as the Fuglede–Putnam theorem. In this paper, we will extend this result to the case in which 𝐴 is an injective (𝑝, 𝑘)-quasihyponormal operator and 𝐵* is a dominant operator. We also show that the same result remains valid for (𝑝, 𝑘)-quasihyponormal and log-hyponormal operators.
Georgian Mathematical Journal – de Gruyter
Published: Sep 1, 2009
Keywords: Fuglede–Putnam theorem; (𝑝, 𝑘)-quasihyponormal operator; dominant operator
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