Non-natural topologies on spaces of holomorphic functions
Volume 108 / 2013
Annales Polonici Mathematici 108 (2013), 215-217
MSC: Primary 46E10; Secondary 46A04, 32A70.
DOI: 10.4064/ap108-3-1
Abstract
It is shown that every proper Fréchet space with weak$^*$-separable dual admits uncountably many inequivalent Fréchet topologies. This applies, in particular, to spaces of holomorphic functions, solving in the negative a problem of Jarnicki and Pflug. For this case an example with a short self-contained proof is added.
