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Fuglede-Putnam's theorem for \boldmath p-hyponormal or \boldmath \rm{log}-hyponormal operators

Published online by Cambridge University Press:  26 February 2003

Atsushi Uchiyama  and
Kôtarô Tanahashi
Atsushi Uchiyama
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan email: uchiyama@math.tohoku.ac.jp
Kôtarô Tanahashi
Affiliation:
Department of Mathematics, Tohoku Pharmaceutical University, Sendai 981-8558, Japan email: tanahasi@tohoku-pharm.ac.jp
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 397 - 410
Copyright
2002 Glasgow Mathematical Journal Trust