Journal of Operator Theory
Volume 85, Issue 1, Winter 2021 pp. 135-151.
The cyclic group and the transpose of an
R-cyclic matrix
Authors:
Octavio Arizmendi (1), James A. Mingo (2)
Author institution: (1) Centro de Investigacion en Matematicas,
Guanajuato, Mexic
(2) Department
of Mathematics and Statistics, Queen's University, Jeffery
Hall, Kingston, Ontario, K7L 3N6, Canada
Summary: We show that using the cyclic group the transpose of an
R-cyclic matrix can be decomposed along diagonal parts
into a sum of parts which are freely independent over
diagonal scalar matrices. Moreover, if the R-cyclic matrix
is self-adjoint then the off-diagonal parts are
R-diagonal.
DOI: http://dx.doi.org/10.7900/jot.2019oct09.2281
Keywords: free probability, R-diagonal operators, R-cyclic operators
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