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Zeitschrift für Analysis und ihre Anwendungen

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Volume 9, Issue 4, 1990, pp. 319–326
DOI: 10.4171/ZAA/404

Published online: 1990-08-31

On Uniform Limitability and Banach Limits

Peter Schatte[1]

(1) Bergakademie Freiberg, Germany

A bounded sequence is shown to be $H_{nifty}$-limitable to the value $a$ 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 $M$ of bounded sequences. More general uniform limitation methods can be characterized in a similar manner.

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Schatte Peter: On Uniform Limitability and Banach Limits. Z. Anal. Anwend. 9 (1990), 319-326. doi: 10.4171/ZAA/404