Abstract
We generalize features of bounded symmetric domains to a bigger class of symmetric spaces calledMakarevic spaces: we associate a generalizedBergman operator to such a space and describe the invariant pseudo-metric and the invariant measure on the space by means of this family of operators. The space itself can be characterized essentially as the domain where the generalized Bergman operator is nondegenerate. These results are applied to the theory ofcompactly causal symmetric spaces: we describe explicitly the complex domain Ξ associated to such a space.
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