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http://dx.doi.org/10.4134/JKMS.j150701

BESSEL MULTIPLIERS AND APPROXIMATE DUALS IN HILBERT C∗ -MODULES  

Azandaryani, Morteza Mirzaee (Department of Mathematics University of Qom)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1063-1079 More about this Journal
Abstract
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.
Keywords
Hilbert $C^*$-module; Bessel multiplier; approximate duality; modular Riesz basis;
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