Means on dyadic symmetric sets and polar decompositions. (English) Zbl 1146.51301
Summary: 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.
Keywords:
symmetric space; symmetric set; midpoint; geometric mean; loop; spectral mean; polar decompositionReferences:
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