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We say operators A, B on Hilbert space satisfy Fuglede-Putnam theorem if AX = X B for some X implies . We show that if either (1) A is p-hyponormal and is a class y operator or (2) A is a class y operator and is p-hyponormal, then A, B satisfy Fuglede-Putnam theorem.

FUGLEDE-PUTNAM THEOREM FOR p-HYPONORMAL OR CLASS y OPERATORS