Joint Numerical Radius Of Spherical Aluthge Transforms Of Tuples Of Hilbert Space Operators

Let T = (T-1, ..., T-d) be a d-tuple of operators on a complex Hilbert space H. The spherical Aluthge transform of T is the d -tuple given by (T) over cap := (root PV1 root P, ..., root PVd root P) where P := root T-1*T-1 + ... + T-d*T-d and (V-1, ..., V-d) is a joint partial isometry such that T-k = VkP for all 1 <= k <= d. In this paper, we prove several inequalities involving the joint numerical radius and the joint operator norm of (T) over cap . Moreover, a characterization of the joint spectral radius of an operator tuple T via n-th iterated of spherical Aluthge transform is established.