What is claimed is:1. A computer-implemented method comprising:receiving, via a processor, instructions to switch an operational context of a dynamic address translation (DAT) structure to a new operational context;determining, via the processor, if context switching has been enabled by a bit in a control register within the DAT structure;based on determining that context switching is enabled, determining, via the processor, if the new operational context of the DAT structure is different than a current operational context of the DAT structure as specified in the instructions having been received;choosing, via the processor, whether to switch to a full operational context based on the new operational context being different than the current operational context;responsive to the new operational context being the full operational context, responsive to the new operational context being different than the current operational context, and responsive to the context switching being enabled, setting up a full space DAT structure and setting to OFF a private space bit; andresponsive to the full operational context not being used, setting up a partial space DAT structure and setting to ON the private space bit.2. The method according to claim 1, further comprising setting the private space control bit to ON via an address space control element (ASCE).3. The method according to claim 1, further comprising setting the private space control bit to ON via millicode.4. The method according to claim 1, wherein when the private space control bit is set to ON, a common segment bit in the partial space DAT structure is set to OFF.5. The method according to claim 4, wherein when the private space control bit is set to ON, prefixed storage area (PSA) addresses of an address space are non-fetch protected.6. The method according to claim 5, wherein when the PSA addresses of the address space is non-fetch protected, no sensitive data is stored in a first portion of memory for the PSA addresses.7. The method according to claim 1, wherein the DAT structure is created by mapping address spaces in a memory, the full space DAT structure mapping to a full portion segment table that maps to at least one full portion page table that maps to registers, the partial space DAT structure mapping to a partial portion segment table that maps to a partial portion page table that maps to a subset of the registers.8. A system comprising:a memory having computer readable instructions; and one or more processors for executing the computer readable instructions, the computer readable instructions controlling the one or more processors to perform operations comprising:receiving instructions to switch an operational context of a dynamic address translation (DAT) structure to a new operational context;determining if context switching has been enabled by a bit in a control register within the DAT structure;based on determining that context switching is enabled, determining if the new operational context of the DAT structure is different than a current operational context of the DAT structure as specified in the instructions having been received;choosing whether to switch to a full operational context based on the new operational context being different than the current operational context;responsive to the new operational context being the full operational context, responsive to the new operational context being different than the current operational context, and responsive to the context switching being enabled, setting up a full space DAT structure and setting to OFF a private space bit; andresponsive to the full operational context not being used, setting up a partial space DAT structure and setting to ON the private space bit.9. The system according to claim 8, wherein the operations further comprise setting the private space control bit to ON via an address space control element (ASCE).10. The system according to claim 8, wherein the operations further comprise setting the private space control bit to ON via millicode.11. The system according to claim 8, wherein when the private space control bit is set to ON, a common segment bit in the partial space DAT structure is set to OFF.12. The system according to claim 11, wherein when the private space control bit is set to ON, prefixed storage area (PSA) addresses of an address space are non-fetch protected.13. The system according to claim 12, wherein when the PSA addresses of the address space is non-fetch protected, no sensitive data is stored in a first portion of memory for the PSA addresses.14. The system according to claim 8, wherein the dynamic address translation (DAT) structure is created by mapping address spaces in a memory.15. A computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to perform operations comprising:receiving instructions to switch an operational context of a dynamic address translation (DAT) structure to a new operational context;determining if context switching has been enabled by a bit in a control register within the DAT structure;based on determining that context switching is enabled, determining if the new operational context of the DAT structure is different than a current operational context of the DAT structure;choosing whether to switch to a full operational context based on the new operational context being different than the current operational context;responsive to the new operational context being the full operational context, responsive to the new operational context being different than the current operational context, and responsive to the context switching being enabled, setting up a full space DAT structure and setting to OFF a private space bit; andresponsive to the full operational context not being used, setting up a partial space DAT structure and setting to ON the private space bit.16. The computer program product according to claim 15, wherein the operations further comprise setting the private space control bit to ON via an address space control element (ASCE).17. The computer program product according to claim 15, wherein the operations further comprise setting the private space control bit to ON via millicode.18. The computer program product according to claim 15, wherein when the private space control bit is set to ON, a common segment bit in the partial space DAT structure is set to OFF.19. The computer program product according to claim 18, wherein when the private space control bit is set to ON, prefixed storage area (PSA) addresses of an address space are non-fetch protected.20. The computer program product according to claim 15, wherein the dynamic address translation (DAT) structure is created by mapping address spaces in a memory.