Unimodular eigenvalues and weak mixing

Lee K. Jones, Michael Lin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Let T be a linear operator on a Banach space X, with sup ∥ Tn ∥ < ∞. If {Tnx} is weak-* sequentially compact in X**, we prove the equivalence of the following: (1) limN → ∞ N-1n = 1N |〈 x*, Tnx〉| = 0 for every x*ε{lunate} X*. (2) x is orthogonal to the eigenvectors of T* with unimodular eigenvalues. For example, the assumption holds if X* is separable. An example shows that the sufficient condition for (1), Tninix → 0 weakly for some {ni}, is not necessary.

Original languageEnglish
Pages (from-to)42-48
Number of pages7
JournalJournal of Functional Analysis
Issue number1
StatePublished - 1 Jan 1980

ASJC Scopus subject areas

  • Analysis


Dive into the research topics of 'Unimodular eigenvalues and weak mixing'. Together they form a unique fingerprint.

Cite this