$*$-Bimodules

Abstract: A $$-bimodule for a unital $$-algebra $A$ is an $A$-bimodule $X$ which is a vector space with involution $x\mapsto x^+$ satisfying $(a\cdot x\cdot b)^+=b^+\cdot x^+\cdot b^+$ for $x\in X$ and $a,b\in A$. An algebraic model for $$-bimodules is given. Hilbert space representations of $$-bimodules are defined and studied. A GNS-like representation theorem is obtained.