1. CJM 2007 (vol 59 pp. 795)
 Jaworski, Wojciech; Neufang, Matthias

The ChoquetDeny Equation in a Banach Space
Let $G$ be a locally compact group and $\pi$ a representation of
$G$ by weakly$^*$ continuous isometries acting in a dual Banach space $E$.
Given a
probability measure $\mu$ on $G$, we study the ChoquetDeny equation
$\pi(\mu)x=x$, $x\in E$. We prove that the solutions of this equation
form the range of a projection of norm $1$ and can be represented by means of a
``Poisson formula'' on the same boundary space that is used to represent the
bounded harmonic functions of the random walk of law $\mu$. The relation
between the space of solutions of the ChoquetDeny equation in $E$ and the
space of bounded harmonic functions can be understood in terms of a
construction resembling the $W^*$crossed product and coinciding precisely
with the crossed product in the special case of the ChoquetDeny equation in
the space $E=B(L^2(G))$ of bounded linear operators on $L^2(G)$. Other
general properties of the ChoquetDeny equation in a Banach space are also
discussed.
Categories:22D12, 22D20, 43A05, 60B15, 60J50 

2. CJM 1997 (vol 49 pp. 736)