  We are interested in properties, especially injectivity (in the sense of
category theory), of the ternary rings of operators generated by certain
subsets of an inverse semigroup via the regular representation. We determine
all subsets of the extended bicyclic semigroup which are closed under the
triple product $xy^*z$ (called semiheaps) and show that the weakly closed
ternary rings of operators generated by them (W*-TROs) are injective operator
spaces.
