Abstract. A concept of an orthonormal basis for Hilbert $C^*$-modules is discussed. It is proved that each Hilbert $C^*$-module $W$ over an arbitrary $C^*$-algebra ${\cal A}$ of (not necessarily all) compact operators on a Hilbert space possesses an orthonormal basis. The $C^*$-algebra of all adjointable operators on $W$ is naturally represented on a Hilbert space contained in $W$. Also, ``compact" operators on $W$ are characterized.

AMS Subject Classification (1991): 46L05, 46C50

Keyword(s): C^*, -algebra, C^*, Hilbert-module, orthonormal basis, compact operator, adjointable operator

Received September 26, 2000, and in revised form December 20, 2000. (Registered under 2840/2009.)