ON THE CLOSURE OF LINEAR COMBINATION OF TWO SUBALGEBRAS OF CONTINUOUS FUNCTIONS

Let A be a set of continuous real or complex functions defined on a compact K. In this work we study conditions for which the closure (A) over bar is the algebra C(K) of all continuous functions on K. In [1] the case of a subalgebra of real functions and in [2] the case when A is a lattice that is the sum of two subalgebras of real functions were considered. For complex functions, see also [1] for the case when A is the sum of a subalgebra and its complex adjoint one and, simultaneously, (A) over bar is a subalgebra itself. Here we consider the cases of the sum of two subalrebras and of linear combinations of two subalgebras.