1
Department of Mathematics Faculty of Chemistry University of Bucharest Bd. Regina Elisabeta nr. 4--12, Bucharest Romania University of Bucharest Bd. Regina Elisabeta nr. 4--12, Bucharest Romania
In this paper we study the unitary equivalence between Hilbert modules over a locally \documentclass{aastex}
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$C^{*}$
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Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally \documentclass{aastex}
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$C^{*}$
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that a Hilbert module over a Fr\'{e}chet locally \documentclass{aastex}
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$C^{*}$
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$C^{*}$
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of all ``compact'' operators has an approximate unit.