>It is my curiousity to know if i issue command "expire inventory" should TSM 
>database space increase ?

Observe the invocation options as in the Admin Ref manual:
You can invoke it with "Quiet=Yes" to minimize output, realizing that
its actions are logged in the server Activity Log and that the default,
"Quiet=No" results in numerous messages.

In any case, Expire Inventory makes its biggest dent in the Recovery Log.

>p/s I wish i didn't want to use aix smitty to increase the space.

You can try deleting any obsolete filespaces that may be lingering in
your server, or use Set ACTlogretention to reduce the amount of Activity
Log data in the db.

But realize that you may simply be experiencing normal growth, as per
your retention policies, in which case there's no choice but to
expand your configuration.

  Richard Sims, BU