Document Type: Original Article
University Moulay Ismail, Morocco
Universidade Federal de Mato Grosso do Sul, Brazil
In this paper, we build a process in order to extend the truncated weighted shift, using techniques of the bi-indexed recursive sequences. We apply this process to solve the subnormality of $2$-variable weighted shifts, whose associated moment sequence is a bi-indexed recursive sequence. Notably, we detail the case of the truncated $2$-variable weighted shift $T\equiv(T_1, T_2)$ of order $(2,2)$.