Abstract
In this paper, approximate duals and Q-approximate duals of standard Bessel sequences are studied, where Q is a bounded (not necessarily adjointable) operator on a Hilbert \(C^*\)-module. Particularly, we consider the stability of Q-approximate duals under morphisms of Hilbert \(C^*\)-modules and also their stability under small perturbations is discussed. Then, we get some properties of (a, m)-approximate duals in Hilbert \(C^*\)-modules. These approximate duals are defined 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. Moreover, using multipliers for pair Bessel sequences, the notion of (a, m)-approximate duality is generalized for the cases that the sequences are non-Bessel or m is not necessarily a symbol.
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Mirzaee Azandaryani, M. Approximate Duals, Q-Approximate Duals and Morphisms of Hilbert \(C^*\)-Modules. Iran J Sci Technol Trans Sci 44, 1685–1694 (2020). https://doi.org/10.1007/s40995-020-00984-3
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DOI: https://doi.org/10.1007/s40995-020-00984-3