SELF-ADJOINT INTERPOLATION ON AX = Y IN ALGL

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 = for any f and g in . (2) There exists a self-adjoint operator A in Alg such that AX = Y.