Means on dyadic symmetrie sets and polar decompositions
In this paper we develop the theory of the geometric mean and the spectral mean on dyadic symmetric sets, an algebraic generalization of symmetric spaces of noncompact type, and apply them to obtain decomposition theorems of involutive systems. In particular we show for involutive dyadic symmetric sets: every involutive dyadic symmetric set admits a canonical polar decomposition with factors the geometric and spectral means.
2000 Mathematics Subject Classification51F15 20N05 20F50 20K25
Key words and phrasessymmetric space symmetric set midpoint mean loop spectral mean polar decomposition
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