  This article begins with a study of convex effect-state spaces. We point out
that such spaces are equivalent to interval effect algebras that generate an
ordered linear space and possess an order-determining set of states. We then
discuss operations and instruments on interval effect algebras under the
assumption of an unrestrictive condition. Effects measured by operations and
sequential products of effects relative to operations are considered.
Observables are introduced and coexistence of effects are discussed. We also
present properties of sequential products of observables and conditioning of
observables related to instruments. The final section is devoted to Holevo
instruments. Pure and mixed Holevo operations are defined and extended to
instruments. The Holevo sequential product of two observables is defined and
the marginals of these products are computed. We define the commutant of two
effects and derive its properties. Examples are given that illustrate the
properties of previously presented concepts.
