Semidefinite extreme points of the unit ball in a polynomial space

Let Δ be the triangle in R 2 bounded by the lines x = 0 , y = 0 , x + y = 1 (the standard simplex in R 2 ). Denote by π 2 the set of all real bivariate algebraic polynomials of total degree at most two. Let B Δ be the unit ball of the space π 2 endowed with the supremum norm on Δ . e a full description of the semidefinite extreme points of B Δ . The present paper completes the description of the set E Δ of all extreme points of B Δ started in Milev and Naidenov (2008) [13] and Milev and Naidenov (2011) [14]. We study, as an application, the path-connectedness of E Δ . The conclusion is that E Δ ∖ { ± 1 } consists of two path-connected components.