REMARKS ON THE WILANSKY PROPERTY

摘要

A separableFK-spaceEhas the Wilansky Property if wheneverFis anFK-space contained and dense inEwithF#x3B2;=E#x3B2;thenF=E.In 1987 G. Bennett and W. Stadler independently showed that ifEandEBare bothBk#x2014;AKspaces thenEhas the Wilansky Property. In 1990 D. Noll relaxed theAKcondition by arguing ifE, EfareBk#x2014;Adspaces and ifE#x3B2;is separable thenEhas the Wilansky Property. In this note we show that Noll's result is in fact equivalent to the original Bennett/Stadler result.