Clifford Algebra And M(?)bius Transformation On Hilbert Space

In the first part of this paper,we give the definition and properites of Clifford algebra in the Hilbert space H,and the definition of Clifford matrice,which generates sense-preserving Mo|¨bius transformations in H;In the second part of this paper,we discuss the sufficient and necessary condition which guarantees the existence of a Mo|¨bius transformation g actiong on H.The uniqueness of g is also discussed.