Naslov
A note on Blecher's characterization of Hilbert C*-modules

Autori
Bruckler, F.M.

Izvornik
Glasnik matematički (0017-095X) 36(56) (2001); 263-269

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
C*-module; adjointable operators; strict topology; compact operators; Hilbert space

Sažetak
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 $\h$ such that $V$ can be embedded in the algebra $B(\H, \h)$ of bounded operators between $\H$ and $\h$. In this paper it is shown: For a Hilbert $C^*$-module over a $C^*$-algebra of compact operators the Hilbert space $\h$ coincides with a Hilbert subspace of the module, which characterizes all adjointable operators on the module. For any Hilbert $C^*$-module $V$, its strict completion can be realized in the algebra $B(\H, \h)$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA