  It is proposed the scheme of quantum mechanics, in which a Hilbert space and
the linear operators are not primary elements of the theory. Instead of it
certain variant of the algebraic approach is considered. The elements of
noncommutative algebra (observables) and the nonlinear functionals on this
algebra (physical states) are used as the primary constituents. The functionals
associate with results of a particular measurement. It is suggested to consider
certain ensembles of the physical states as quantum states of the standart
quantum mechanics. It is shown that in such scheme the mathematical formalism
of the standart quantum mechanics can be reproduced completely.
