you can use the select * from summary
when summary is a table that holds all conclusions of your last backups
this gives you backup,archive,restore,retrive and much more info about what occured on your TSM server during the last 10 days i think but you can increase or decrease the retention of the info there
i think its the simplest of ways to get that info.
might as well generate a report through TSM MANAGER if you have one
it basically does the same only the SQL query is built in.
Best regards!