On multiple polynomials of Capelli type

This paper deals with the class of Capelli polynomials in free associative algebra $F\{Z\}$ (where $F$ is an arbitrary field, $Z$ is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their $T$-ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.