JournalszaaVol. 9, No. 4pp. 319–326

On Uniform Limitability and Banach Limits

  • Peter Schatte

    Bergakademie Freiberg, Germany
On Uniform Limitability and Banach Limits cover
Download PDF

Abstract

A bounded sequence is shown to be HniftyH_{nifty}-limitable to the value aa if and only if all strong Banach limits assign the same value a to this sequence. In this connection, a strong Banach limit means a linear functional with certain properties on the space MM of bounded sequences. More general uniform limitation methods can be characterized in a similar manner.

Cite this article

Peter Schatte, On Uniform Limitability and Banach Limits. Z. Anal. Anwend. 9 (1990), no. 4, pp. 319–326

DOI 10.4171/ZAA/404