Hypercyclic Operators on Hilbert C*-modules
Stefan Ivkovic
TL;DR
This paper characterizes hypercyclic and chaotic operators on Hilbert C*-modules, providing necessary and sufficient conditions, along with concrete examples, expanding understanding of operator dynamics in this setting.
Contribution
It introduces new characterizations of hypercyclic and chaotic operators on Hilbert C*-modules and non-unital C*-algebras, with explicit examples and conditions.
Findings
Characterization of hypercyclic bilateral weighted shift operators
Necessary and sufficient conditions for chaos
Concrete examples of hypercyclic operators
Abstract
In this paper, we characterize hypercyclic generalized bilateral weighted shift operators on the standard Hilbert module over the C*-algebra of compact operators on the separable Hilbert space. Moreover, we give necessary and sufficient conditions for these operators to be chaotic and we provide concrete examples. In addition, we characterize a class of hypercyclic operators on non-unital C*-algebras and we provide concrete examples.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Advanced Topics in Algebra