SUBMODULES OF COMMUTATIVE C*-ALGEBRAS

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 ∞ ‫)ޔ(‬ to the non-commutative setting. Considering these subspaces as C(‫-)ޔ‬modules contained in L ∞ ‫,)ޔ(‬ we show that under some restrictions, a similar description can be given for the B-submodules of A, where A is a C * -algebra and B is a commutative C * -subalgebra of A. We use this to give a description of the ‫ލ‬ n (B)-submodules of ‫ލ‬ n (A).2010 Mathematics Subject Classification. 46L99, 47A15, 47L30.