See Faraut & Koranyi (1994, pp. 73, 202–203) and Rudin (1973, pp. 270–273). By finite-dimensionality, every point in the convex span of S is the convex combination of n + 1 points, where n = 2 dim E. So the convex span of S is already compact and equals the closed unit ball. Faraut, J.; Koranyi, A. (1994), Analysis on symmetric cones, Oxford Mathematical Monographs, Oxford University Press, ISBN978-0198534778Rudin, Walter (1973). Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 25 (First ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN9780070542259.
This article uses as its main sources Jordan, von Neumann & Wigner (1934), Koecher (1999) and Faraut & Koranyi (1994), adopting the terminology and some simplifications from the latter. Jordan, P.; von Neumann, J.; Wigner, E. (1934), "On an algebraic generalization of the quantum mechanical formalism", Annals of Mathematics, 35 (1): 29–64, doi:10.2307/1968117, JSTOR1968117 Koecher, M. (1999), The Minnesota Notes on Jordan Algebras and Their Applications, Lecture Notes in Mathematics, vol. 1710, Springer, ISBN978-3540663607 Faraut, J.; Koranyi, A. (1994), Analysis on symmetric cones, Oxford Mathematical Monographs, Oxford University Press, ISBN978-0198534778
This article uses as its main sources Jordan, von Neumann & Wigner (1934), Koecher (1999) and Faraut & Koranyi (1994), adopting the terminology and some simplifications from the latter. Jordan, P.; von Neumann, J.; Wigner, E. (1934), "On an algebraic generalization of the quantum mechanical formalism", Annals of Mathematics, 35 (1): 29–64, doi:10.2307/1968117, JSTOR1968117 Koecher, M. (1999), The Minnesota Notes on Jordan Algebras and Their Applications, Lecture Notes in Mathematics, vol. 1710, Springer, ISBN978-3540663607 Faraut, J.; Koranyi, A. (1994), Analysis on symmetric cones, Oxford Mathematical Monographs, Oxford University Press, ISBN978-0198534778
