Abstract
The Aluthge transformation is generalized in the viewpoint of the axiom of operator means by using double operator integrals. It includes the mean transformation which is defined by S. H. Lee, W. Y. Lee and J. Yoon. Next we shall give some properties of it. Especially, we shall show that the n-th iteration of mean transformation of an invertible matrix converges to a normal matrix. Inclusion relations among numerical ranges of induced Aluthge transformations by some operator means are considered.
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