An improved formulation of some theorems and axioms in the axiomatic foundation of the Hilbert space structure of quantum mechanics

In Ref. [1] the axiomatic foundation of the Hilbert space structure of quantum mechanics was outlined. Apart from a set of physically plausible axioms, the (mathematical) assumption (V 1) of the minimal-decomposition property of the basenorm spaceB was incorporated into the axiomatic scheme of the theory.It is shown in the present paper that the assumption (V 1) is superfluous. In the first part of the paper we give a short summary of the axioms; in the second part the main theorems are proved without using assumption (V 1).