A Dichotomy Principle for Universal Series

Volume 56 / 2008

V. Farmaki, V. Nestoridis Bulletin Polish Acad. Sci. Math. 56 (2008), 93-104 MSC: Primary 05D10, 41A58; Secondary 30B30. DOI: 10.4064/ba56-2-1

Abstract

Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin–Prikry, we show that for every sequence $(\alpha_{j})_{j=1}^{\infty}$ of scalars, there exists a subsequence $(\alpha_{k_j})_{j=1}^{\infty}$ such that either every subsequence of $(\alpha_{k_j})_{j=1}^{\infty}$ defines a universal series, or no subsequence of $(\alpha_{k_j})_{j=1}^{\infty}$ defines a universal series. In particular examples we decide which of the two cases holds.

Authors

  • V. FarmakiDepartment of Mathematics
    Athens University
    Panepistemiopolis
    15784 Athens, Greece
    e-mail
  • V. NestoridisDepartment of Mathematics
    Athens University
    Panepistemiopolis
    15784 Athens, Greece
    and
    Department of Mathematics and Statistics
    University of Cyprus
    1678 Nicosia, Cyprus
    e-mail

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