Powers of R-diagonal Elements
نویسنده
چکیده
We prove that if (a; b) is an R-diagonal pair in some non-commutative probability space (A; ') then (a p ; b p) is R-diagonal too and we compute the determining series f (a p ;b p) in terms of the distribution of ab. We give estimates of the upper and lower bounds of the support of free multiplicative convolution of probability measures compactly supported on 0; 1, and use the results to give norm estimates of powers of R-diagonal elements in nite von Neumann algebras. Finally we compute norms, distributions and R-transforms related to powers of the circular element.
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