Extension of the truncated bi-indexed weighted shifts, recursiveness and subnormality. (English) Zbl 07064109

Taher, Rajae Ben; Rachidi, Mustapha

Adv. Oper. Theory 4, No. 4, 836-851 (2019).

Summary: 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 \((2,2)\).

MSC:

47B37	Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B20	Subnormal operators, hyponormal operators, etc.
65Q30	Numerical aspects of recurrence relations

Keywords:

2-variable weighted shifts; bi-indexed generalized Fibonacci sequence; representing measure; truncated 2-variable moment problem; subnormaliy