BESSEL MULTIPLIERS AND APPROXIMATE DUALS IN HILBERT C* -MODULES

Two standard Bessel sequences in a Hilbert C* -module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert C* -module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the C* -algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m) -approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.