BANACH SPACES , OPERATORS AND ALGEBRAS Abstracts of talks

The origin of Korovkin Approximation theory is the classical theorem of P.P. Korovkin (1953),which says that for a sequence (Tn) of positive linear operators on C[a, b], in order to conclude the uniform convergence of Tnf to f for all f ∈ C[a, b], it suffices to check the uniform convergence only for the three functions f ∈ {1, x, x2}. Starting from this beautiful result many mathematicians have worked to extend it to other function spaces, or more generally to abstract spaces such as Banach spaces, Banach lattices and Banach algebras. We confine to the theory developed in commutative Banach algebras only. Mainly we are interested in certain commutative Banach algebras (defined on locally compact groups) studied in harmonic analysis. We present some of our contribution in this direction.