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Hilbert C$^*-$modules in which all closed submodules are complemented

Author: Bojan Magajna
Journal: Proc. Amer. Math. Soc. 125 (1997), 849-852
MSC (1991): Primary 46L05; Secondary 46C50
MathSciNet review: 1346981
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Abstract: Let $B$ be a C$^*-$algebra. If there exists a full Hilbert $B-$module $X$ such that $X=Y\oplus Y^{\perp }$ for each closed submodule $Y$, then $B$ is *-isomorphic to a C$^*-$algebra of (not neccesarily all) compact operators on a Hilbert space.

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Additional Information

Bojan Magajna

Keywords: Hilbert C$^*-$modules, complemented submodules
Received by editor(s): July 3, 1995
Received by editor(s) in revised form: September 26, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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