It depends on your definition of file virtualization. If the definition is broad enough, it might include HSM capabilities....
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Embracing ILM is a bit trickier, because ILM is so broadly defined already.
Generally speaking, one of the basic premises of HSM is the ability to archive or move data to another location. HSM leaves a stub file where the data was so that the application "thinks" the data is still there. At the same time, we define virtualization as having emulation, aggregation and abstraction attributes. Well, we've emulated the file's presence, and I'd say that falls into the realm of virtualization.
This is slightly different from archiving (aka data movement), in which the files and directories are moved completely.
Go to the beginning of the File Virtualization FAQ Guide.