Some properties of the mapping T_{\mu} introduced by a representation in Banach and locally convex spaces


Let  \mathcal{S}=\{T_{s}:s\in S\} be a representation of a semigroup S. We show that the mapping T_{\mu} introduced by a mean on a subspace of l^{\infty}(S) inherits some properties of \mathcal{S} in Banach spaces and locally convex spaces. The notions of Q-G-nonexpansive mapping and Q-G-attractive point in locally convex spaces are introduced. We prove that T_{\mu} is a Q-G-nonexpansive mapping when T_{s} is Q-G-nonexpansive mapping for each s\in S and a point in a locally convex space is Q-G-attractive point of T_{\mu} if it is a Q-G-attractive point of  \mathcal{S}.

DOI Code: 10.1285/i15900932v40n1p101

Keywords: Representation; Nonexpansive; Attractive point; Directed graph; Mean

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