Abstract:Motivated by the concept of pseudo-Riesz sequences and pseudo- Riesz bases in Hilbert spaces, recently introduced by Biswas and Mitkovski, in this paper, we study pseudo-Riesz sequences and pseudo-Riesz bases in the standard Hilbert module over a unital C*-algebra. We prove that a Bessel sequence in the standard Hilbert C*-module is a pseudo-Riesz sequence if and only if the associated synthesis operator is upper semi-C*-Fredholm. Moreover, we introduce a new notion of pseudo-Riesz-Weyl sequences in Hilbert C*-modules and we prove that a Bessel sequence in the standard Hilbert C*-module is pseudo-Riesz-Weyl if and only if the associated synthesis operator is upper semi-C*-Weyl. We apply the obtained results in the study of perturbations of Bessel sequences in Hilbert C*-modules.
From: Stefan Ivkovic [view email]
[v1]
Mon, 15 Jun 2026 11:46:00 UTC (12 KB)
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