TL;DR
This paper demonstrates the existence of algebras of hypercyclic vectors for certain classes of operators, advancing understanding of hypercyclicity in functional analysis.
Contribution
It establishes the existence of hypercyclic algebras for convolution, composition, and backward shift operators, which was previously unknown.
Findings
Hypercyclic algebras exist for convolution operators.
Hypercyclic algebras exist for composition operators.
Hypercyclic algebras exist for backward shift operators.
Abstract
We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Algebraic and Geometric Analysis