  We describe a scheme of quantum mechanics in which the Hilbert space and
linear operators are only secondary structures of the theory. As primary
structures we consider observables, elements of noncommutative algebra, and the
physical states, the nonlinear functionals on this algebra, which associate
with results of single measurement. We show that in such scheme the
mathematical apparatus of the standard quantum mechanics does not contradict a
hypothesis on existence of an objective local reality, a principle of a
causality and Kolmogorovian probability theory.
