n-FOLD JORDAN PRODUCT COMMUTING MAPS WITH A lambda-ALUTHGE TRANSFORM

Abstract

Let B(H) be the set of all bounded linear operators from H to H, where H is a complex Hilbert space. In this paper, we study the properties of T when the lambda-Aluthge transform of T-n is T . Also we prove that the bijective map Phi: B(H) -> B(K) commutes with a lambda-Aluthge transform under the n -fold jordan product if and only if there exists an unitary operator U :H -> K such that Phi(T)= UTU* for every T in B(H).