Positive continuous linear functionals on Riesz spaces and applications to minimax theorems

The paper is concerned with minimax results for functions taking values in an order-complete topological Riesz space. The idea is that of deriving minimax equalities from scalar ones, by means of infinitely many weak equalities. Consequently a large variety of Riesz-valued versions of well known minimax results is stated under standard conditions, but with the extra assumption that extrema (i.e. greatest lower bounds and least upper bounds) are assumed to be cluster points of the range of the involved function.