SELF-ADJOINT INTERPOLATION ON AX = Y IN ALGL Jo, Young-Soo; 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 article, we showed the following : Let be a subspace lattice acting on a Hilbert space and let X and Y be operators in . Let P be the projection onto . If FE = EF for every , then the following are equivalent: (1) < , , and < Xf, Yg >=< Yf,Xg > for any f and g in . (2) There exists a self-adjoint operator A in Alg such that AX = Y.