UNITARY INTERPOLATION ON AX = Y IN ALG Kang, Joo-Ho;
Given operators X and Y acting on a Hilbert space , an interpolating operator is a bounded operator A such that AX = Y. In this paper, we showed the following : Let be a subspace lattice acting on a Hilbert space and let and be operators in B() for i = 1, 2, . Let be the projection onto for all i = 1, 2, . If = for some k in and all E in , then the following are equivalent: (1) < range , and < >=< > for some k in and for all f and g in . (2) There exists an operator A in Alg such that = for i = 1, 2, and AA = I = AA.