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.)
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