Co-analytic, right-invertible operators are supercyclic

• Autorzy: Sameer Chavan
• Języki publikacji: EN

Abstrakty

EN

Let 𝓗 denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space 𝓗, let 𝓑(𝓗) denote the algebra of bounded linear operators on 𝓗. We show that for any co-analytic, right-invertible T in 𝓑(𝓗), αT is hypercyclic for every complex α with $|α| > β^{-1}$, where $β ≡ inf_{||x||=1}||T*x|| > 0$. In particular, every co-analytic, right-invertible T in 𝓑(𝓗) is supercyclic.

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 47B20: Subnormal operators, hyponormal operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 119
• Numer: 1
• Strony: 137-142

Daty

wydano

2010

Twórcy

autor

Sameer Chavan

• Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Kanpur 208016, India

Identyfikatory

DOI

10.4064/cm119-1-9