Hilbert spaces as a specific instrument for process control

Hilbert spaces are representing an individual class of abstract mathematical spaces within functional analysis. Hilbert space is infinite dimensional complex space with inner conjunction. Points of this space are functions and by their coordinates is arranged an infinite sequence of functional values of these functions at a certain interval. Algebraic structure of such spaces is giving a place to define, quantify and then analyze geometric relationships between functions which are the vectors of Hilbert space. An aim of the article is to refer to usage of Hilbert space as a state space of process represented by suitable acquired information signal. Space structures are giving a place to classify status of the process and also monitor its dynamics.