Thank you for your answere!
I first installed ADE 1.7.2. successfuly. Deauthorized and authorized my computer - just for being sure. I connected my prs-t1 but still it did not appear in the library.
Then I updated the firmware provided on http://www.sony.at/support/de/product/PRS-T1 or http://esupport.sony.com/US/p/model-home.pl?mdl=PRST1&template_id=1&re gion_id=1&tab=download#/downloadTab . This firmware update included a programm called Reader for PC (which replaced Reader Library). This programm is connected to my ADE-library and that way I am able to transfer my books to the reader. The driver was not the problem - the firmware was the key to the riddle.
Mission accomplished - thank you so very much!!!