2001/03/13 by Fabio Zucca
Mathematics · #math.PR #math.FA #msc:60J15 #msc:60J45
published as Extracta Mathematicae, 17 n.2 (2002), 201-209 · 9 pages
arxiv created 2001/03/13 · arxiv updated 2009/11/30
We study a general transition operator, generated by a random walk on a graph X; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from l^∞(X) into itself. Moreover we characterize compact operators and we relate this property to the behaviour of the associated random walk. We give a necessary and sufficient condition for the pre-adjoint of the discrete Laplace operator to be an injective map.