UNITARY INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG𝓛 Kang, Joo Ho;
Given vectors x and y in a separable complex Hilbert space , an interpolating operator is a bounded operator A such that Ax = y. We show the following: Let be a tridiagonal algebra on and let and be vectors in . Then the following are equivalent: (1) There exists a unitary operator in such that Ax = y. (2) There is a bounded sequence in such that and for .