The correctness of a shared object, which can be accessed by several processes concurrently, is specified through two different kinds of properties - safety and liveness. When implementing a shared object it is important to specify its correctness in a such way that it should be feasible under given assumptions. In this work we study the question of implementability of shared objects that satisfy certain safety and liveness properties under certain assumptions. In particular, we study implementability of liveness properties of transactional memory (TM) shared objects with strict serializability, a strong safety property. TM allows a programmer to encapsulate pieces of sequential code within transactions that run concurrently and it ensures that transactions run in some consistent manner by committing or aborting them. First, we give a formal definition of a liveness property in the TM context. Then, we proceed to show that certain classes of liveness properties of TM can not be implemented with strict serializability in a system in which processes are prone to failures. We also show that, in general, we cannot find a weakest non-implementable (resp. strongest implementable) liveness of TM when we require some common safety property like strict serializability. Moreover, we generalize this result to other shared object types and give a characterization of safety properties for which we can find weakest non-implementable (resp. strongest implementable) liveness. In addition to correctness properties we study the limitations of parallelism which affects performance and scalability of implementations. Specifically, we show that we cannot implement a TM which guarantees disjoint-access parallelism, which say that transactions do not need to synchronize unless they access the same application objects, while guaranteeing very weak safety and the weakest non-blocking liveness.