A secured subspace facility is provided for ensuring isolated storage for transactions running under an operating system main task. Isolation is achieved by attaching, from an operating system task, subtasks that will restrict application addressing. The attaching includes defining a subspace address environment as home space within a dispatchable unit access list (DU-AL) associated with each attached subtask. Multiple subtasks can be attached with each subtask running applications in an isolated address subspace, notwithstanding execution of the applications in address register addressing mode.