COMPACT INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG 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. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. We show the following : Let Alg be a tridiagonal algebra on a separable complex Hilbert space and let x = and y = be vectors in H. Then the following are equivalent: (1) There exists a compact operator A = in Alg such that Ax = y. (2) There is a sequence in such that converges to zero and for all k , .