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Time regularity and functions of the Volterra operator

Volume 220 / 2014

Zoltán Léka Studia Mathematica 220 (2014), 1-14 MSC: Primary 47A10, 47A30, 47B38; Secondary 47G10. DOI: 10.4064/sm220-1-1

Abstract

Our aim is to prove that for any fixed $1/2 < \alpha < 1$ there exists a Hilbert space contraction $T$ such that $\sigma(T) = \{1\}$ and $$ \|T^{n+1} - T^n\| \asymp n^{-\alpha} \quad (n \geq 1). $$ This answers Zemánek's question on the time regularity property.

Authors

  • Zoltán LékaDepartment of Mathematics
    Ben Gurion University of the Negev
    P.O.B. 653
    Beer Sheva 84105, Israel
    and
    Alfréd Rényi Institute of Mathematics
    Hungarian Academy of Sciences
    13–15, Reáltanoda u.
    1053 Budapest, Hungary
    e-mail
    e-mail

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