Hypercyclic sequences of operators

• Autorzy: Fernando León-Saavedra , Vladimír Müller
• Języki publikacji: EN

Abstrakty

EN

A sequence (Tₙ) of bounded linear operators between Banach spaces X,Y is said to be hypercyclic if there exists a vector x ∈ X such that the orbit Tₙx is dense in Y. The paper gives a survey of various conditions that imply the hypercyclicity of (Tₙ) and studies relations among them. The particular case of X = Y and mutually commuting operators Tₙ is analyzed. This includes the most interesting cases (Tⁿ) and (λₙTⁿ) where T is a fixed operator and λₙ are complex numbers. We also study when a sequence of operators has a large (either dense or closed infinite-dimensional) manifold consisting of hypercyclic vectors.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47A16: Cyclic vectors, hypercyclic and chaotic operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 1
• Strony: 1-18

Daty

wydano

2006

Twórcy

autor

Fernando León-Saavedra

• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Pol. Rio San Pedro S/N, 1500 Puerto Real, Spain

autor

Vladimír Müller

• Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

Identyfikatory

DOI

10.4064/sm175-1-1