SUBMODULES OF COMMUTATIVE C*-ALGEBRAS

In this paper we generalise a result of Izuchi and Suarez (K. Izuchi and D. Suarez, Norm-closed invariant subspaces in L-infinity and H-infinity, GlasgowMath. J. 46 (2004), 399-404) on the shift invariant subspaces of L-infinity(T) to the non-commutative setting. Considering these subspaces as C(T)-modules contained in L-infinity(T), we show that under some restrictions, a similar description can be given for the B-submodules of 2L, where 2L is a C*-algebra and B is a commutative C*-subalgebra of A. We use this to give a description of the M-n(B)-submodules of M-n(A).