Modular Riesz bases versus Riesz bases in Hilbert $C^*$-Modules
Marzieh Hasannasab
TL;DR
This paper characterizes modular Riesz bases in Hilbert C*-modules, highlighting their similarities and differences with classical Riesz bases in Hilbert spaces, including the existence of exact frames that are not modular Riesz bases.
Contribution
It provides new characterizations of modular Riesz bases and compares their properties with those of Riesz bases in Hilbert spaces, revealing key differences.
Findings
Modular Riesz bases share many properties with classical Riesz bases.
There exist exact frames that are not modular Riesz bases.
The paper offers new characterizations of modular Riesz bases.
Abstract
In this paper, we give new characterizations of modular Riesz bases in Hilbert -modules. We prove that modular Riesz bases share many properties with Riesz bases in Hilbert spaces. Moreover we show that there are also important differences; for example, there exist exact frames that are not modular Riesz bases.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Medical Imaging Techniques and Applications · Advanced Operator Algebra Research