1. A computer program product for facilitating management of system memory of a computing environment, the computer program product comprising: a non-transitory computer readable storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising: based on executing a Call Logical Processor (CLP) instruction for enabling an adapter and requesting a specific number of direct memory access (DMA) address spaces to be assigned to the adapter, the CLP instruction comprising an operation code to specify a call logical processor operation, an indication of a requested number of DMA address spaces to be assigned to the adapter, the indication of the requested number of DMA address spaces to be assigned to the adapter comprising the specific number of DMA address spaces requested to be assigned to the adapter, and a function handle to identify the adapter on behalf of which the instruction is being performed, the function handle having an adapter not enabled indicator, enabling the adapter, assigning one or more DMA address spaces of the requested specific number of DMA address spaces to the adapter, and returning the function handle having an adapter enabled indicator; based on executing a Modify PCI Function Controls (MPFC) instruction that specifies a register address translation parameters operation, defining at least one DMA address space of the one or more DMA address spaces assigned to the adapter; receiving a request from the adapter to access system memory; and using a requestor identifier and an address space identifier provided in the request to select a DMA address space to be used in the access, the DMA address space being selected from the one or more DMA address spaces assigned to the adapter.