Bombal Gordón, FernandoVera Boti, Gabriel2023-06-212023-06-211973BOMBAl, F.: Medidas invariantes con valores en A-módulos normados. Tesis Doctoral. Memorias del Instituto Jorge-Juan, C. S. I. C., Madrid. DIXMIER, J.: Les moyennes invariantes dans les semigroupes et leurs applications. Act. Sci. Math. Szeged, 12 A, 1950, 213-227. GREENLEAF, F. P. : Invariant means on topological groups. Van Nostrand, New York, 1969. HEWITT, E. AND Ross, K. A.: Abstract Harmonic Analysis, vol I. SprillgerVerlag, Berlin, 1963. HORVÁTH, J.: Topological Vector Spaces and Distributions, volI. Addison-Vesley, Reading, Massachusetts, 1966. KÖTHE, G.: Topological Vector Spaces, 1. Springer-Verlag, Berlin, 1969. NACHBIN, L.: Elements of approximation theory. Van Nostrand, Princeton, 1967. RODRIGUEZ-SALINAS, B.: El problema de la medida. Memorias del Instituto Jorge-Juan, C. S. 1. C., Madrid. SCHAEFER, H.: Topological Vector Spaces. Springer-Verlag, Berlín, 1971. VERA, G.: Limites generalizados en A-módulos. Tesis Doctoral. Aparecerá en las Memorias del Instituto Jorge-Juan, C. S. 1. C., Madrid.0010-0757https://hdl.handle.net/20.500.14352/64738Let S be a semigroup and let E be a locally convex topological vector space over the field of real numbers. Let B(S,E) be the linear space of mappings f:S→E such that f(S) is a bounded set of E . For every s∈S and every f∈B(S,E), s f[f s ] denotes the function from S into E defined by ( s f)(T)=f(s⋅t) for each t∈S [(f s )(t)=f(t⋅s) for each t∈S ]. A subspace X of B(S,E) is left [right] invariant if, for every f∈X and s∈S , s f[f s ] also belongs to X . The space X is invariant if it is both left and right invariant. The authors give the following definition of a mean: a mean μ on a subspace X of B(S,E) , containing the constant functions, is a linear mapping of X into E such that μ(f) belongs to the closed convex hull of f(S) . Moreover. if X is left [right] invariant, μ is left [right] invariant provided μ( s f)=μ(f)[μ(f s )=μ(f)] , for every f∈X and s∈S . If X is invariant and μ is left and right invariant, then μ is invariant. The authors study the problem of the existence of invariant means on certain subspaces of X . For a larger class of semigroups they prove that if E is quasicomplete for the Mackey topology, a necessary and sufficient condition to ensure the existence of a invariant mean on B(S,E) is that E be semi-reflexive.spajournal articlehttp://www.collectanea.ub.edu/index.php/Collectanea/article/view/3416/4096http://www.collectanea.ub.edu/index.php/Collectanea/open access517.98Means on groupsLocally convex spacesAnálisis funcional y teoría de operadores