Geodesic
Fuglede-Putnam's theorem for \boldmath p-hyponormal or \boldmath \rm{log}-hyponormal operators
Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 397-410

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Let T be p-hyponormal or \rm{log}-hyponormal on a Hilbert space H. Then we have XT=T^*X whenever XT^*=TX for some X \in \scriptstyle{B}(\scriptstyle{H}). This is an extension of Patel's result. Also for p-hyponormal or \rm{log}-hyponormal T^*, dominant S and any X \in \scriptstyle{B}(\scriptstyle{H}) such that XT=SX, we have XT^*=S^*T. 
Uchiyama, Atsushi; Tanahashi, Kôtarô. Fuglede-Putnam's theorem for \boldmath p-hyponormal or \boldmath \rm{log}-hyponormal operators. Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 397-410. doi: 10.1017/S0017089502030057
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     title = {Fuglede-Putnam's theorem for \boldmath p-hyponormal or \boldmath \rm{log}-hyponormal operators},
     journal = {Glasgow mathematical journal},
     pages = {397--410},
     year = {2002},
     volume = {44},
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     doi = {10.1017/S0017089502030057},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502030057/}
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