Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): 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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