It is my belief that JESUS inspired the deciples, especially Peter. When in JESUS' company, Peter was filled with a great sense of faith and belief. As an example, think back to when he attempted to walk on water to his master.

When JESUS was no longer present, Peter's faith waivered, which is completely understandable and human. Nonetheless, JESUS loved them and he appeared to them after his death, his greeting to them was one of peace and love.