Abstract. Using the technique of adjoining an order unit to a normed linear space, we have characterized strictly convex spaces among normed linear spaces and Hilbert spaces among strictly convex Banach spaces, respectively. This leads to a generalization of spin factors and provides a new class of absolute order unit spaces.

DOI: 10.14232/actasm-021-785-5

AMS Subject Classification (1991): 46B40; 46B20

Keyword(s): adjoining an order unit, strictly convex space, absolutely ordered space, absolute order unit space, $JB$-algebra, spin factor

received 5.3.2021, revised 19.4.2021, accepted 30.7.2021. (Registered under 35/2021.)