International Journal of Pure and Applied Mathematics ————————————————————————– Volume 23 No. 1 2005, 87-90 A NOTE ON OPERATORS CONJUGATE TO d-HOMOMORPHISMS ¨ Omer G¨ ok Department of Mathematics Faculty of Arts and Sciences Yıldız Technical University Davutpa¸ sa Campus, Istanbul, 34210, TURKEY e-mail: gok@yildiz.edu.tr Abstract: Let X, Y be two Banach f -modules over the same Banach f - algebra A and suppose that T is an A-orthomorphism continuous linear operator from X into Y . It is shown that T ′ ∈ dh(Y ′ ,X ′ ), where T ′ is the continuous adjoint of T . AMS Subject Classification: 47B60, 47B65 Key Words: Banach f -module, f -algebra, Banach lattice, order ideal 1. Introduction Let X be a Banach space and A be a Banach f -algebra with unit. By L(X) we denote the set of all continuous linear operators from X into X. We say that X is a Banach f -module if there exists a bilinear mapping p : A × X → X, (a, x) → a.x satisfying the following conditions: (i) 1.x = x for all x ∈ X, 1 ∈ A; (ii) (ab).x = a.(b.x) for all a, b ∈ A, x ∈ X; (iii) ‖a.x‖≤‖a‖‖x‖ for all a ∈ A, x ∈ X. Bilinear mapping p induces m : A → L(X), (a, x) → m(a)x = a.x is a unital norm ‖.‖ to SOT (the strong operator topology) continuous algebra homomorphism. We let X ′ denote the dual of a Banach X. We can establish Received: July 12, 2005 c  2005, Academic Publications Ltd.