Strong stability conjecture under double commutation on the synthesis kernel
Let HHH be a Hilbert space, let T1,T2∈B(H)T_1,T_2\in B(H)T1,T2∈B(H) commute, and suppose that T1iT2jφi,j≥0\\{T_1^iT_2^j\varphi\\}_{i,j\geq 0}T1iT2jφi,j≥0 is an overcomplete frame for HHH. Let R1R_1R1 and R2R_2R2 be the assoc…