A new generalization of Aluthge transform for tuples of operators

Abstract

In this paper, -spherical Aluthge transform for the tuples of operators is introduced, as an extension of the classical Aluthge transform, and its continuity in the norm topology is given. Using this transform, we generalize and refine the numerical radius inequality given by Feki and Yamazaki. In the case that the operator tuples are commutative, we establish the Taylor spectral equality via this new transform. To extend the results of Chabbabi and Mbekhta to the case of the commuting operator tuples involving this transform, we give the sufficient and necessary condition for this transform being contractive. In addition, some new characterizations of the joint normaloid tuples are given, which lead to a new proof of Ch's well-known result on the jointly normal tuples.