#### Glasnik Matematicki, Vol. 36, No.2 (2001), 263-269.

### A NOTE ON BLECHER'S CHARACTERIZATION OF
HILBERT C^{*}-MODULES

### Franka Miriam Brückler

Department of Mathematics, P.O. Box 335,
10002 Zagreb, Croatia

*e-mail:* `bruckler@math.hr`

**Abstract.** By a theorem of D. P. Blecher, a Hilbert
C*-module *V* over a C*-algebra
A (faithfully and
nondegenerately represented on a Hilbert space
H) is characterized by a
certain Hilbert space
H_{V},
such that *V* can be embedded in the algebra
*B*(H,
H_{V})
of bounded operators between
H and
H_{V}.
In this paper it is shown: 1. For a Hilbert C*-module
over a C*-algebra of compact operators the Hilbert space
H_{V}
conicides with a Hilbert subspace of the module, which characterizes
all adjointable operators on the module; 2. For any Hilbert
C*-module *V*, its strict completion can be
realized in the algebra
*B*(H,
H_{V}).

**1991 Mathematics Subject Classification.**
46L08.

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