Positive Interpolation on AX=Y in a Tridiagonal Algebra Alg L = Positive Interpolation on AX=Y in a Tridiagonal Algebra Alg L

다국어 초록 (Multilingual Abstract)

Given operators X and Y acting on a separable Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. We show the following : Let AlgL be a tridiagonal algebra on a separable complex Hilbert space H and let X = (x_(ij)) and Y = (y_(ij)) be operators acting on H. Then the following are equivalent:
(1) There exists a positive operator A = (a_(ij)) in AlgL such that AX = Y.
(2) There is a non-negative real bounded sequence {α_(n)} such that y_(ij) = α_(i)x_(ij) for i,j ∈ N.