TY - JOUR
T1 - Boundaries for strong Schur spaces
AU - Dutta, S.
AU - Fonf, V. P.
N1 - Funding Information:
V.P.F. was supported in part by ISF grant 209/09.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - It is known that if a Banach space X does not contain an isomorphic copy of c0, then for any boundary B and representation B =U∞ n=1 Bn such that the sequence Bn is increasing, there exist an indexmand somer > 0 such thatBm is r-norming forX. In this note, we showthat if someBm is uniformly norming, that is, there existsr > 0 not depending on a boundary B and a representation B = ∪ Bn, then that property characterizes Strong Schur spaces.
AB - It is known that if a Banach space X does not contain an isomorphic copy of c0, then for any boundary B and representation B =U∞ n=1 Bn such that the sequence Bn is increasing, there exist an indexmand somer > 0 such thatBm is r-norming forX. In this note, we showthat if someBm is uniformly norming, that is, there existsr > 0 not depending on a boundary B and a representation B = ∪ Bn, then that property characterizes Strong Schur spaces.
UR - http://www.scopus.com/inward/record.url?scp=84907004058&partnerID=8YFLogxK
U2 - 10.1093/qmath/hat041
DO - 10.1093/qmath/hat041
M3 - Article
AN - SCOPUS:84907004058
SN - 0033-5606
VL - 65
SP - 887
EP - 891
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 3
ER -