POSITIVE INTERPOLATION ON Ax = y AND AX = Y IN ALG Kang, Joo-Ho;
Let be a subspace lattice on a Hilbert space . Let x and y be vectors in and let be the projection onto sp(x). If = for each E , then the following are equivalent. (1) There exists an operator A in Alg such that Ax = y, Af = 0 for all f in and A 0. (2) sup < < x, y > 0. Let X and Y be operators in . Let P be the projection onto . If PE = EP for each E , then the following are equivalent: (1) sup < and < Xf, Yf > 0 for all f in H. (2) There exists a positive operator A in Alg such that AX = Y.