A Study of the Furstenberg Boundary for Pair of Groups

Authors
Mohammad Bagher Asadi
Zahra Hassanpour-Yakhdani
University of Tehran
Abstract
In this paper, assuming that G is a discrete topological group and H is a subgroup of G, we introduce the notion of a (G, H)-operator system and define the Hamana boundary for pairs of groups (G, H). In fact, we show that the Furstenberg boundary for pairs of groups is isomorphic to the Hamana boundary for pairs of groups. In other words, the natural extension of the classical theory of Furstenberg boundaries remains valid for the Furstenberg boundary associated with pairs of groups (G, H).
Keywords
Furstenberg boundary
Hamana boundary
Injective envelope
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