Although there is no support from Logitech mouse works wonderfully well under Linux (Debian Wheezy). If after a suspend or reboot no connection is established, a small adjustment in the system is needed.
In the file /usr/share/gnome-bluetooth/pin-code-database.xml following line must be added:
On my old Logitech Travel Mouse this was not necessary. For this, the M557 is better in the hand.