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We define what it means for a state in a convex cone of states on a space ofobservables to be generalized-entangled relative to a subspace of theobservables, in a general ordered linear spaces framework for operationaltheories. This extends the notion of ordinary entanglement in quantuminformation theory to a much more general framework. Some important specialcases are described, in which the distinguished observables are subspaces ofthe observables of a quantum system, leading to results like the identificationof generalized unentangled states with Lie-group-theoretic coherent states whenthe special observables form an irreducibly represented Lie algebra. Some openproblems, including that of generalizing the semigroup of local operations withclassical communication to the convex cones setting, are discussed.Comment: 19 pages, to appear in proceedings of Quantum Structures VII, Int. J.  Theor. Phy

A Generalization of Entanglement to Convex Operational Theories: Entanglement Relative to a Subspace of Observables