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Paper's Title:

On Commutator of Aluthge Transforms and Fuglede-Putnam Property


(Manzar Maleki, Ali Reza Janfada and Seyed Mohammad Sadegh Nabavi Sales

International Campus, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad,

Faculty of Mathematics and Statistics, Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,

Department of Pure Mathematics, Hakim Sabzevari University,
P.O. Box 397, Sabzevar,


We deal with the well-known Fuglede-Putnam theorem and related FP-property. We show that if (A,B) has the FP-property, then so has where 0 t1,t21 are arbitrary. We first prove that if and only if AX=XB for all X, whenever (A,B) has the FP-property. We prove some similar results for instead of $ as well. Also we introduce the sequence of generalized iterations of Aluthge transform of operators and express some results for this notion associated to the FP-property.

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