Geodesic
SUBMODULES OF COMMUTATIVE C*-ALGEBRAS
Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 471-479

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we generalise a result of Izuchi and Suárez (K. Izuchi and D. Suárez, Norm-closed invariant subspaces in L∞ and H∞, Glasgow Math. J. 46 (2004), 399–404) on the shift invariant subspaces of $L^\infty(\mathbb{T})$ to the non-commutative setting. Considering these subspaces as $C(\mathbb{T})$-modules contained in $L^\infty(\mathbb{T})$, we show that under some restrictions, a similar description can be given for the ${\mathfrak{B}}$-submodules of ${\mathfrak{A}}$, where ${\mathfrak{A}}$ is a C*-algebra and ${\mathfrak{B}}$ is a commutative C*-subalgebra of ${\mathfrak{A}}$. We use this to give a description of the $\mathbb{M}_n({\mathfrak{B}})$-submodules of $\mathbb{M}_n({\mathfrak{A}})$.
DOI : 10.1017/S0017089513000402
Mots-clés : 46L99, 47A15, 47L30 
MIHEISI, NAZAR. SUBMODULES OF COMMUTATIVE C*-ALGEBRAS. Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 471-479. doi: 10.1017/S0017089513000402
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