RT Journal Article
T1 Polynomial compactness in Banach spaces
A1 Biström, Peter
A1 Jaramillo Aguado, Jesús Ángel
A1 Lindström, Mikael
AB We investigate infinite dimensional Banach spaces equipped with the initial topology with respect to the continuous polynomials. We show nonlinear properties for this topology in both the real and the complex case. A new property for Banach spaces, polynomial Dunford-Pettis property, is introduced. For spaces with this property the compact sets in the topology induced by the polynomials are shown to be invariant under the summation map. For most real Banach spaces we characterize the polynomially compact sets as the bounded sets that are separated from zero by the positive polynomials.
PB Rocky Mt Math Consortium
SN 0035-7596
YR 1998
FD 1998
LK https://hdl.handle.net/20.500.14352/57601
UL https://hdl.handle.net/20.500.14352/57601
LA eng
NO DGICYT (Spain)
DS Docta Complutense
RD 4 abr 2025