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SUBMODULES OF COMMUTATIVE C*-ALGEBRAS

  • NAZAR MIHEISI (a1)

Abstract

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 $\mathbb{M}_n({\mathfrak{A}})$ .

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References

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1.Dixmier, J., C*-algebras (North-Holland, New York, NY, 1969).
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SUBMODULES OF COMMUTATIVE C*-ALGEBRAS

  • NAZAR MIHEISI (a1)

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